pymatgen.symmetry package

Submodules

pymatgen.symmetry.analyzer module

An interface to the excellent spglib library by Atsushi Togo (https://github.com/spglib/spglib) for pymatgen.

v1.0 - Now works with both ordered and disordered structure. v2.0 - Updated for spglib 1.6. v3.0 - pymatgen no longer ships with spglib. Instead, spglib (the python

version) is now a dependency and the SpacegroupAnalyzer merely serves as an interface to spglib for pymatgen Structures.

class PointGroupAnalyzer(mol: Molecule, tolerance: float = 0.3, eigen_tolerance: float = 0.01, matrix_tolerance: float = 0.1)[source]

Bases: object

A class to analyze the point group of a molecule.

The general outline of the algorithm is as follows:

1. Center the molecule around its center of mass.

2. Compute the inertia tensor and the eigenvalues and eigenvectors.

3. Handle the symmetry detection based on eigenvalues.

   1. Linear molecules have one zero eigenvalue. Possible symmetry operations are C*v or D*v

   2. Asymmetric top molecules have all different eigenvalues. The maximum rotational symmetry in such molecules is 2

   3. Symmetric top molecules have 1 unique eigenvalue, which gives a unique rotation axis. All axial point groups are possible except the cubic groups (T & O) and I.

   4. Spherical top molecules have all three eigenvalues equal. They have the rare T, O or I point groups.

Attribute:

sch_symbol (str): Schoenflies symbol of the detected point group.

The default settings are usually sufficient.

Parameters:

• mol (Molecule) – Molecule to determine point group for.

• tolerance (float) – Distance tolerance to consider sites as symmetrically equivalent. Defaults to 0.3 Angstrom.

• eigen_tolerance (float) – Tolerance to compare eigen values of the inertia tensor. Defaults to 0.01.

• matrix_tolerance (float) – Tolerance used to generate the full set of symmetry operations of the point group.

get_equivalent_atoms()[source]

Get sets of equivalent atoms with symmetry operations.

Returns:

with two possible keys:

eq_sets: A dictionary of indices mapping to sets of indices, each key maps to

indices of all equivalent atoms. The keys are guaranteed to be not equivalent.

sym_ops: Twofold nested dictionary. operations[i][j] gives the symmetry

operation that maps atom i unto j.

Return type:

dict

get_pointgroup() → PointGroupOperations[source]

Get a PointGroup object for the molecule.

get_rotational_symmetry_number() → int[source]

Get rotational symmetry number.

Returns:

Rotational symmetry number.

Return type:

int

get_symmetry_operations() → Sequence[SymmOp][source]

Get symmetry operations.

Returns:

symmetry operations in Cartesian coord.

Return type:

list[SymmOp]

inversion_op = SymmOp(self.affine_matrix=array([[-1., -0., -0.,  0.],        [-0., -1., -0.,  0.],        [-0., -0., -1.,  0.],        [-0., -0., -0.,  1.]]))[source]

is_valid_op(symm_op: SymmOp) → bool[source]

Check if a particular symmetry operation is a valid symmetry operation for a molecule, i.e., the operation maps all atoms to another equivalent atom.

Parameters:

symm_op (SymmOp) – Symmetry operation to test.

Returns:

True if SymmOp is valid for Molecule.

Return type:

bool

symmetrize_molecule() → dict[source]

Get a symmetrized molecule.

The equivalent atoms obtained via get_equivalent_atoms() are rotated, mirrored… unto one position. Then the average position is calculated. The average position is rotated, mirrored… back with the inverse of the previous symmetry operations, which gives the symmetrized molecule

Returns:

with three possible keys:

sym_mol: A symmetrized molecule instance. eq_sets: A dictionary of indices mapping to sets of indices, each key maps to indices

of all equivalent atoms. The keys are guaranteed to be not equivalent.

sym_ops: Twofold nested dictionary. operations[i][j] gives the symmetry operation

that maps atom i unto j.

Return type:

dict

class PointGroupOperations(sch_symbol: str, operations: Sequence[SymmOp], tol: float = 0.1)[source]

Bases: list

Represents a point group, which is a sequence of symmetry operations.

sch_symbol[source]

Schoenflies symbol of the point group.

Type:

str

Parameters:

• sch_symbol (str) – Schoenflies symbol of the point group.

• operations ([SymmOp]) – Initial set of symmetry operations. It is sufficient to provide only just enough operations to generate the full set of symmetries.

• tol (float) – Tolerance to generate the full set of symmetry operations.

class SpacegroupAnalyzer(structure: Structure, symprec: float | None = 0.01, angle_tolerance: float = 5)[source]

Bases: object

Takes a pymatgen Structure object and a symprec.

Uses spglib to perform various symmetry finding operations.

Parameters:

• structure (Structure | IStructure) – Structure to find symmetry

• symprec (float) – Tolerance for symmetry finding. Defaults to 0.01, which is fairly strict and works well for properly refined structures with atoms in the proper symmetry coordinates. For structures with slight deviations from their proper atomic positions (e.g., structures relaxed with electronic structure codes), a looser tolerance of 0.1 (the value used in Materials Project) is often needed.

• angle_tolerance (float) – Angle tolerance for symmetry finding. Defaults to 5 degrees.

find_primitive(keep_site_properties: bool = False) → Structure[source]

Find a primitive version of the unit cell.

Parameters:

keep_site_properties (bool) – Whether to keep the input site properties (including magnetic moments) on the sites that are still present after the refinement. Note: This is disabled by default because the magnetic moments are not always directly transferable between unit cell definitions. For instance, long-range magnetic ordering or antiferromagnetic character may no longer be present (or exist in the same way) in the returned structure. If keep_site_properties is True, each site retains the same site property as in the original structure without further adjustment.

Returns:

A primitive cell in the input cell is searched and returned as a Structure object. If no primitive cell is found, None is returned.

get_conventional_standard_structure(international_monoclinic: bool = True, keep_site_properties: bool = False) → Structure[source]

Get a structure with a conventional cell according to certain standards. The standards are defined in Setyawan, W., & Curtarolo, S. (2010). High-throughput electronic band structure calculations: Challenges and tools. Computational Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010 They basically enforce as much as possible norm(a1)<norm(a2)<norm(a3). NB This is not necessarily the same as the standard settings within the International Tables of Crystallography, for which get_refined_structure should be used instead.

Parameters:

• international_monoclinic (bool) – Whether to convert to proper international convention such that beta is the non-right angle.

• keep_site_properties (bool) – Whether to keep the input site properties (including magnetic moments) on the sites that are still present after the refinement. Note: This is disabled by default because the magnetic moments are not always directly transferable between unit cell definitions. For instance, long-range magnetic ordering or antiferromagnetic character may no longer be present (or exist in the same way) in the returned structure. If keep_site_properties is True, each site retains the same site property as in the original structure without further adjustment.

Returns:

The structure in a conventional standardized cell

get_conventional_to_primitive_transformation_matrix(international_monoclinic: bool = True) → NDArray[source]

Get the transformation matrix to transform a conventional unit cell to a primitive cell according to certain standards the standards are defined in Setyawan, W., & Curtarolo, S. (2010). High-throughput electronic band structure calculations: Challenges and tools. Computational Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010.

Parameters:

international_monoclinic (bool) – Whether to convert to proper international convention such that beta is the non-right angle.

Returns:

Transformation matrix to go from conventional to primitive cell

get_crystal_system() → CrystalSystem[source]

Get the crystal system for the structure, e.g. (triclinic, orthorhombic, cubic, etc.).

Raises:

ValueError – on invalid space group numbers < 1 or > 230.

Returns:

Crystal system for structure

Return type:

str

get_hall() → str[source]

Get Hall symbol for structure.

Returns:

Hall symbol

Return type:

str

get_ir_reciprocal_mesh(mesh: tuple[int, int, int] = (10, 10, 10), is_shift: tuple[float, float, float] = (0, 0, 0)) → list[tuple[Kpoint, float]][source]

k-point mesh of the Brillouin zone generated taken into account symmetry. The method returns the irreducible kpoints of the mesh and their weights.

Parameters:

• mesh (3x1 array) – The number of kpoint for the mesh needed in each direction

• is_shift (3x1 array) – Whether to shift the kpoint grid. (1, 1,

• 0.5 (1) means all points are shifted by)

• 0.5

• 0.5.

Returns:

A list of irreducible kpoints and their weights as a list of tuples [(ir_kpoint, weight)], with ir_kpoint given in fractional coordinates

get_ir_reciprocal_mesh_map(mesh: tuple[int, int, int] = (10, 10, 10), is_shift: tuple[float, float, float] = (0, 0, 0)) → tuple[NDArray, NDArray][source]

Same as ‘get_ir_reciprocal_mesh’ but the full grid together with the mapping that maps a reducible to an irreducible kpoint is returned.

Parameters:

• mesh (3x1 array) – The number of kpoint for the mesh needed in each direction

• is_shift (3x1 array) – Whether to shift the kpoint grid. (1, 1,

• 0.5 (1) means all points are shifted by)

• 0.5

• 0.5.

Returns:

A tuple containing two numpy.ndarray. The first is the mesh in fractional coordinates and the second is an array of integers that maps all the reducible kpoints from to irreducible ones.

get_kpoint_weights(kpoints: Sequence[Kpoint], atol: float = 1e-05) → list[float][source]

Calculate the weights for a list of kpoints.

Parameters:

• kpoints (Sequence) – Sequence of kpoints. np.arrays is fine. Note that the code does not check that the list of kpoints provided does not contain duplicates.

• atol (float) – Tolerance for fractional coordinates comparisons.

Returns:

List of weights, in the SAME order as kpoints.

get_lattice_type() → LatticeType[source]

Get the lattice for the structure, e.g. (triclinic, orthorhombic, cubic, etc.).This is the same as the crystal system with the exception of the hexagonal/rhombohedral lattice.

Raises:

ValueError – on invalid space group numbers < 1 or > 230.

Returns:

Lattice type for structure

Return type:

str

get_point_group_operations(cartesian: bool = False) → list[SymmOp][source]

Return symmetry operations as a list of SymmOp objects. By default returns fractional coord symm ops. But Cartesian can be returned too.

Parameters:

cartesian (bool) – Whether to return SymmOps as Cartesian or direct coordinate operations.

Returns:

Point group symmetry operations.

Return type:

list[SymmOp]

get_point_group_symbol() → str[source]

Get the point group associated with the structure.

Returns:

Point group for structure.

Return type:

Pointgroup

get_primitive_standard_structure(international_monoclinic: bool = True, keep_site_properties: bool = False) → Structure[source]

Get a structure with a primitive cell according to certain standards. The standards are defined in Setyawan, W., & Curtarolo, S. (2010). High-throughput electronic band structure calculations: Challenges and tools. Computational Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010.

Parameters:

• international_monoclinic (bool) – Whether to convert to proper international convention such that beta is the non-right angle.

• keep_site_properties (bool) – Whether to keep the input site properties (including magnetic moments) on the sites that are still present after the refinement. Note: This is disabled by default because the magnetic moments are not always directly transferable between unit cell definitions. For instance, long-range magnetic ordering or antiferromagnetic character may no longer be present (or exist in the same way) in the returned structure. If keep_site_properties is True, each site retains the same site property as in the original structure without further adjustment.

Returns:

The structure in a primitive standardized cell

get_refined_structure(keep_site_properties: bool = False) → Structure[source]

Get the refined structure based on detected symmetry. The refined structure is a conventional cell setting with atoms moved to the expected symmetry positions.

Parameters:

keep_site_properties (bool) – Whether to keep the input site properties (including magnetic moments) on the sites that are still present after the refinement. Note: This is disabled by default because the magnetic moments are not always directly transferable between unit cell definitions. For instance, long-range magnetic ordering or antiferromagnetic character may no longer be present (or exist in the same way) in the returned structure. If keep_site_properties is True, each site retains the same site property as in the original structure without further adjustment.

Returns:

Refined structure.

get_space_group_number() → int[source]

Get the international spacegroup number (e.g., 62) for structure.

Returns:

International spacegroup number for structure.

Return type:

int

get_space_group_operations() → SpacegroupOperations[source]

Get the SpacegroupOperations for the Structure.

Returns:

SpacegroupOperations object.

get_space_group_symbol() → str[source]

Get the spacegroup symbol (e.g., Pnma) for structure.

Returns:

Spacegroup symbol for structure.

Return type:

str

get_symmetrized_structure() → SymmetrizedStructure[source]

Get a symmetrized structure. A symmetrized structure is one where the sites have been grouped into symmetrically equivalent groups.

Returns:

pymatgen.symmetry.structure.SymmetrizedStructure object.

get_symmetry_dataset() → SpglibDataset[source]

Get the symmetry dataset as a SpglibDataset.

Returns:

With the following properties:

number: International space group number international: International symbol hall: Hall symbol transformation_matrix: Transformation matrix from lattice of

input cell to Bravais lattice L^bravais = L^original * Tmat origin shift: Origin shift in the setting of “Bravais lattice” rotations, translations: Rotation matrices and translation vectors. Space group operations are obtained by [(r,t) for r, t in zip(rotations, translations)]

wyckoffs: Wyckoff letters

Return type:

frozen dict

get_symmetry_operations(cartesian: bool = False) → list[SymmOp][source]

Return symmetry operations as a list of SymmOp objects. By default returns fractional coord sym_ops. But Cartesian can be returned too.

Returns:

symmetry operations.

Return type:

list[SymmOp]

is_laue() → bool[source]

Check if the point group of the structure has Laue symmetry (centrosymmetry).

class SpacegroupOperations(int_symbol: str, int_number: int, symmops: Sequence[SymmOp])[source]

Bases: list

Represents a space group, which is a collection of symmetry operations.

Parameters:

• int_symbol (str) – International symbol of the spacegroup.

• int_number (int) – International number of the spacegroup.

• symmops ([SymmOp]) – Symmetry operations associated with the spacegroup.

are_symmetrically_equivalent(sites1: set[PeriodicSite], sites2: set[PeriodicSite], symm_prec: float = 0.001) → bool[source]

Given two sets of PeriodicSites, test if they are actually symmetrically equivalent under this space group. Useful, for example, if you want to test if selecting atoms 1 and 2 out of a set of 4 atoms are symmetrically the same as selecting atoms 3 and 4, etc.

One use is in PartialRemoveSpecie transformation to return only symmetrically distinct arrangements of atoms.

Parameters:

• sites1 ([PeriodicSite]) – 1st set of sites

• sites2 ([PeriodicSite]) – 2nd set of sites

• symm_prec (float) – Tolerance in atomic distance to test if atoms are symmetrically similar.

Returns:

True if the two sets of sites are symmetrically equivalent.

Return type:

bool

exception SymmetryUndeterminedError[source]

Bases: ValueError

An Exception for when symmetry cannot be determined. This might happen when, for example, atoms are very close together.

cluster_sites(mol: Molecule, tol: float, give_only_index: bool = False) → tuple[Site | None, dict][source]

Cluster sites based on distance and species type.

Parameters:

• mol (Molecule) – Molecule with origin at center of mass.

• tol (float) – Tolerance to use.

• give_only_index (bool) – Whether to return only the index of the origin site, instead of the site itself. Defaults to False.

Returns:

origin_site is a site at the center

of mass (None if there are no origin atoms). clustered_sites is a dict of {(avg_dist, species_and_occu): [list of sites]}

Return type:

tuple[Site | None, dict]

generate_full_symmops(symmops: Sequence[SymmOp], tol: float) → Sequence[SymmOp][source]

Recursive algorithm to permute through all possible combinations of the initially supplied symmetry operations to arrive at a complete set of operations mapping a single atom to all other equivalent atoms in the point group. This assumes that the initial number already uniquely identifies all operations.

Parameters:

• symmops (list[SymmOp]) – Initial set of symmetry operations.

• tol (float) – Tolerance for detecting symmetry.

Returns:

Full set of symmetry operations.

Return type:

list[SymmOp]

iterative_symmetrize(mol: Molecule, max_n: int = 10, tolerance: float = 0.3, epsilon: float = 0.01) → dict[Literal['sym_mol', 'eq_sets', 'sym_ops'], Molecule | dict][source]

Get a symmetrized molecule.

The equivalent atoms obtained via PointGroupAnalyzer.get_equivalent_atoms are rotated, mirrored… unto one position. Then the average position is calculated, which is rotated, mirrored… back with the inverse of the previous symmetry operations, giving the symmetrized molecule.

Parameters:

• mol (Molecule) – A pymatgen Molecule instance.

• max_n (int) – Maximum number of iterations.

• tolerance (float) – Tolerance for detecting symmetry with PointGroupAnalyzer.

• epsilon (float) – If the element-wise absolute difference of two subsequently symmetrized structures is smaller epsilon, the iteration stops before max_n is reached.

Returns:

sym_mol: A symmetrized Molecule instance. eq_sets: A dictionary of indices mapping to sets of indices, each key maps to indices

of all equivalent atoms. The keys are guaranteed to be not equivalent.

sym_ops: Two-fold nested dictionary. operations[i][j] gives the symmetry operation

that maps atom i unto j.

Return type:

dict with three keys

pymatgen.symmetry.bandstructure module

A class for interacting with KPath classes to generate high-symmetry k-paths using different conventions.

class HighSymmKpath(structure, has_magmoms=False, magmom_axis=None, path_type='setyawan_curtarolo', symprec=0.01, angle_tolerance=5, atol=1e-05)[source]

Bases: KPathBase

This class generates path along high symmetry lines in the Brillouin zone according to different conventions. The class is designed to be used with a specific primitive cell setting. The definitions for the primitive cell used can be found in: Computational Materials Science, 49(2), 299-312. doi:10.1016/j.commatsci.2010.05.010. The space group analyzer can be used to produce the correct primitive structure (method get_primitive_standard_structure(international_monoclinic=False)). Ensure input structure is correct before ‘get_kpoints()’ method is used. See individual KPath classes for details on specific conventions.

Parameters:

• structure (Structure) – Structure object

• has_magmoms (bool) – Whether the input structure contains magnetic moments as site properties with the key ‘magmom.’ Values may be in the form of 3-component vectors given in the basis of the input lattice vectors, in which case the spin axis will default to a_3, the third real-space lattice vector (this triggers a warning).

• magmom_axis (list or numpy array) – 3-component vector specifying direction along which magnetic moments given as scalars should point. If all magnetic moments are provided as vectors then this argument is not used.

• path_type (str) – Chooses which convention to use to generate the high symmetry path. Options are: ‘setyawan_curtarolo’, ‘hinuma’, ‘latimer_munro’ for the Setyawan & Curtarolo, Hinuma et al., and Latimer & Munro conventions. Choosing ‘all’ will generate one path with points from all three conventions. Equivalent labels between each will also be generated. Order will always be Latimer & Munro, Setyawan & Curtarolo, and Hinuma et al. Lengths for each of the paths will also be generated and output as a list. Note for ‘all’ the user will have to alter the labels on their own for plotting.

• symprec (float) – Tolerance for symmetry finding

• angle_tolerance (float) – Angle tolerance for symmetry finding.

• atol (float) – Absolute tolerance used to determine symmetric equivalence of points and lines on the BZ.

property equiv_labels[source]

The correspondence between the kpoint symbols in the Latimer and Munro convention, Setyawan and Curtarolo, and Hinuma conventions respectively. Only generated when path_type = ‘all’.

static get_continuous_path(bandstructure)[source]

Obtain a continuous version of an inputted path using graph theory. This routine will attempt to add connections between nodes of odd-degree to ensure a Eulerian path can be formed. Initial k-path must be able to be converted to a connected graph. See npj Comput Mater 6, 112 (2020). 10.1038/s41524-020-00383-7 for more details.

Parameters:

bandstructure (BandstructureSymmLine) – BandstructureSymmLine object.

Returns:

New BandstructureSymmLine object with continuous path.

Return type:

bandstructure (BandstructureSymmLine)

property label_index[source]

The correspondence between numbers and kpoint symbols for the combined kpath generated when path_type = ‘all’. None otherwise.

property path_lengths[source]

List of lengths of the Latimer and Munro, Setyawan and Curtarolo, and Hinuma conventions in the combined HighSymmKpath object when path_type = ‘all’ respectively. None otherwise.

property path_type[source]

The type of kpath chosen.

pymatgen.symmetry.groups module

Defines SymmetryGroup parent class and PointGroup and SpaceGroup classes. Shyue Ping Ong thanks Marc De Graef for his generous sharing of his SpaceGroup data as published in his textbook “Structure of Materials”.

class PointGroup(**kwargs)[source]

Bases: SymmetryGroup

A Point Group, with generators and symmetry operations.

symbol[source]

Full International or Hermann-Mauguin Symbol.

Type:

str

generators[source]

List of generator matrices. Note that 3x3 matrices are used for Point Groups.

Type:

list

symmetry_ops[source]

Full set of symmetry operations as matrices.

Type:

list

Initialize a Point Group from its international symbol. Please note that only the 32 crystal classes are supported right now.

Parameters:

• int_symbol (str) – International or Hermann-Mauguin Symbol. Please note that the PointGroup object

• group (may have a different setting than specified in the int_symbol as only one setting per point)

• now. (is available right)

classmethod from_space_group(sg_symbol: str) → PointGroup[source]

Instantiate one of the 32 crystal classes from a space group symbol in Hermann Mauguin notation (int symbol or full symbol). Please note that the axes of space group and crystal class may be different.

Parameters:

sg_symbol – space group symbol in Hermann Mauguin notation.

Raises:

AssertionError if a valid crystal class cannot be created –

Returns:

crystal class in Hermann-Mauguin notation.

get_orbit(p: ArrayLike, tol: float = 1e-05) → list[np.ndarray][source]

Get the orbit for a point.

Parameters:

• p – Point as a 3x1 array.

• tol – Tolerance for determining if sites are the same. 1e-5 should be sufficient for most purposes. Set to 0 for exact matching (and also needed for symbolic orbits).

Returns:

Orbit for point.

Return type:

list[array]

is_subgroup(supergroup: PointGroup) → bool[source]

True if this group is a subgroup of the supplied group.

Modification of SymmetryGroup method with a few more constraints.

Parameters:

supergroup (pointGroup) – Supergroup to test.

Returns:

True if this group is a subgroup of the supplied group.

Return type:

bool

is_supergroup(subgroup: PointGroup) → bool[source]

True if this group is a subgroup of the supplied group.

Modification of SymmetryGroup method with a few more constraints.

Parameters:

subgroup (PointGroup) – Subgroup to test.

Returns:

True if this group is a supergroup of the supplied group.

Return type:

bool

property symmetry_ops: set[SymmOp][source]

Returns: List of symmetry operations associated with the group.

class SpaceGroup(**kwargs)[source]

Bases: SymmetryGroup

A SpaceGroup.

symbol[source]

Full International or Hermann-Mauguin Symbol.

Type:

str

int_number[source]

International number.

Type:

int

generators[source]

List of generator matrices. Note that 4x4 matrices are used for Space Groups.

Type:

list

order[source]

Order of Space Group.

Type:

int

Initialize a Space Group from its full or abbreviated international symbol. Only standard settings are supported.

Parameters:

• int_symbol (str) – Full International (e.g., “P2/m2/m2/m”) or Hermann-Mauguin Symbol (“Pmmm”) or abbreviated symbol. The notation is a LaTeX-like string, with screw axes being represented by an underscore. For example, “P6_3/mmc”. Alternative settings can be accessed by adding a “:identifier”. For example, the hexagonal setting for rhombohedral cells can be accessed by adding a “:H”, e.g. “R-3m:H”. To find out all possible settings for a spacegroup, use the get_settings() classmethod. Alternative origin choices can be indicated by a translation vector, e.g. ‘Fm-3m(a-1/4,b-1/4,c-1/4)’.

• hexagonal (bool) – For rhombohedral groups, whether to handle as in hexagonal setting (default) or rhombohedral setting. If the int_symbol of a rhombohedral spacegroup is given with the setting (“(:)H”/”(:)R”), this parameter is overwritten accordingly (please note that the setting is not contained in the symbol attribute anymore).

SG_SYMBOLS: ClassVar[set[str]] = {'A-1', 'A112', 'A112/a', 'A112/m', 'A112/n', 'A11a', 'A11m', 'A11n', 'A12/a1', 'A12/m1', 'A12/n1', 'A121', 'A1a1', 'A1m1', 'A1n1', 'A2122', 'A21am', 'A21ma', 'A222', 'A2aa', 'A2mm', 'Aba2', 'Abaa', 'Abaa:2', 'Abm2', 'Abmm', 'Acaa', 'Acaa:2', 'Acmm', 'Ae2a', 'Ae2m', 'Aea2', 'Aea2(-a,c+1/4,b-1/4)', 'Aea2(a,b+1/4,c-1/4)', 'Aea2(b,-a+1/4,c-1/4)', 'Aea2(b,c+1/4,a-1/4)', 'Aeaa', 'Aeaa:1', 'Aeam', 'Aem2', 'Aem2(-a,c+1/4,b-1/4)', 'Aem2(a,b+1/4,c-1/4)', 'Aem2(b,-a+1/4,c-1/4)', 'Aem2(b,c+1/4,a-1/4)', 'Aema', 'Am2a', 'Am2m', 'Ama2', 'Ama2(-a+1/4,c+1/4,b-1/4)', 'Ama2(-a,c+1/4,b-1/4)', 'Ama2(a+1/4,b+1/4,c-1/4)', 'Ama2(a,b+1/4,c-1/4)', 'Ama2(b+1/4,-a+1/4,c-1/4)', 'Ama2(b+1/4,c+1/4,a-1/4)', 'Ama2(b,-a+1/4,c-1/4)', 'Ama2(b,c+1/4,a-1/4)', 'Amaa', 'Amam', 'Amm2', 'Amm2(-a,c+1/4,b-1/4)', 'Amm2(a,b+1/4,c-1/4)', 'Amm2(b,-a+1/4,c-1/4)', 'Amm2(b,c+1/4,a-1/4)', 'Amma', 'Ammm', 'B-1', 'B112', 'B112/b', 'B112/m', 'B112/n', 'B11b', 'B11m', 'B11n', 'B121/m1', 'B1211', 'B2/b11', 'B2/m11', 'B2/n11', 'B211', 'B2212', 'B222', 'B2eb', 'B2em', 'B2mb', 'B2mm', 'Bb11', 'Bb21m', 'Bb2b', 'Bbab', 'Bbab:2', 'Bbcb', 'Bbcb:2', 'Bbe2', 'Bbeb', 'Bbeb:1', 'Bbem', 'Bbm2', 'Bbmb', 'Bbmm', 'Bm11', 'Bm21b', 'Bm2m', 'Bmam', 'Bmcm', 'Bme2', 'Bmeb', 'Bmm2', 'Bmmb', 'Bmmm', 'Bn11', 'C-1', 'C1', 'C12/c1', 'C12/m1', 'C12/m1(-a-1/4,c+1/4,b)', 'C12/m1(a+2*c,a,b)', 'C12/m1(a+2*c-1/4,a+1/4,b)', 'C12/m1(a+c-1/4,b+1/4,c)', 'C12/m1(a,b,a+2*c)', 'C12/m1(a-1/4,b+1/4,a+2*c)', 'C12/m1(a-1/4,b+1/4,c)', 'C12/m1(b,a+2*c,a)', 'C12/m1(b-1/4,-a+1/4,c)', 'C12/m1(b-1/4,a+2*c+1/4,a)', 'C12/m1(b-1/4,c+1/4,a)', 'C12/m1(b-1/4,c+1/4,a+c)', 'C12/m1(c-1/4,a+1/4,b)', 'C12/m1(c-1/4,a+c+1/4,b)', 'C12/m1(c-1/4,b+1/4,-a)', 'C12/n1', 'C121', 'C121(-a-1/4,c-1/4,b)', 'C121(a+2*c,a,b)', 'C121(a+2*c-1/4,a-1/4,b)', 'C121(a+c-1/4,b-1/4,c)', 'C121(a,b,a+2*c)', 'C121(a-1/4,b-1/4,a+2*c)', 'C121(a-1/4,b-1/4,c)', 'C121(c-1/4,a+c-1/4,b)', 'C121(c-1/4,a-1/4,b)', 'C121(c-1/4,b-1/4,-a)', 'C1c1', 'C1c1(2*a+c,b,c)', 'C1m1', 'C1m1(-a-1/4,c-1/4,b)', 'C1m1(a+2*c,a,b)', 'C1m1(a+2*c-1/4,a-1/4,b)', 'C1m1(a+c-1/4,b-1/4,c)', 'C1m1(a,b,a+2*c)', 'C1m1(a-1/4,b-1/4,a+2*c)', 'C1m1(a-1/4,b-1/4,c)', 'C1m1(b,a+2*c,a)', 'C1m1(b-1/4,-a-1/4,c)', 'C1m1(b-1/4,a+2*c-1/4,a)', 'C1m1(b-1/4,c-1/4,a)', 'C1m1(b-1/4,c-1/4,a+c)', 'C1m1(c-1/4,a+c-1/4,b)', 'C1m1(c-1/4,a-1/4,b)', 'C1m1(c-1/4,b-1/4,-a)', 'C1n1', 'C2/c11', 'C2/m11', 'C2/n11', 'C211', 'C222', 'C2221', 'C222_1', 'C2cm', 'C2eb', 'C2me', 'C2mm', 'Cc11', 'Cc2e', 'Cc2m', 'Ccc2', 'Ccc2(a-1/4,b-1/4,c)', 'Ccc2(b-1/4,c-1/4,a)', 'Ccca', 'Ccca:2', 'Cccb', 'Cccb:2', 'Ccce', 'Ccce:1', 'Cccm', 'Cccm(a,b,c-1/4)', 'Cccm(a-1/4,b-1/4,c)', 'Cccm(b,c,a-1/4)', 'Cccm(b-1/4,c-1/4,a)', 'Cccm(c,a,b-1/4)', 'Cccm(c-1/4,a-1/4,b)', 'Ccm21', 'Ccme', 'Ccmm', 'Cm11', 'Cm2e', 'Cm2m', 'Cmc21', 'Cmc21(-a,c+1/4,b)', 'Cmc21(-a-1/4,c-1/4,b)', 'Cmc21(a,b+1/4,c)', 'Cmc21(a-1/4,b-1/4,c)', 'Cmc21(b,-a+1/4,c)', 'Cmc21(b,c+1/4,a)', 'Cmc21(b-1/4,-a-1/4,c)', 'Cmc21(b-1/4,c-1/4,a)', 'Cmc2_1', 'Cmce', 'Cmce(-a-1/4,c-1/4,b)', 'Cmce(a-1/4,b-1/4,c)', 'Cmce(b-1/4,-a-1/4,c)', 'Cmce(b-1/4,c-1/4,a)', 'Cmce(c-1/4,a-1/4,b)', 'Cmce(c-1/4,b-1/4,-a)', 'Cmcm', 'Cmcm(-a+1/2,c-1/4,b+1/4)', 'Cmcm(-a-1/4,c-1/4,b)', 'Cmcm(a+1/2,b-1/4,c+1/4)', 'Cmcm(a-1/4,b-1/4,c)', 'Cmcm(b+1/2,-a-1/4,c+1/4)', 'Cmcm(b+1/2,c-1/4,a+1/4)', 'Cmcm(b-1/4,-a-1/4,c)', 'Cmcm(b-1/4,c-1/4,a)', 'Cmcm(c+1/2,a-1/4,b+1/4)', 'Cmcm(c+1/2,b-1/4,-a+1/4)', 'Cmcm(c-1/4,a-1/4,b)', 'Cmcm(c-1/4,b-1/4,-a)', 'Cmm2', 'Cmm2(2*c,a,b)', 'Cmm2(a-1/4,b-1/4,c)', 'Cmm2(b-1/4,c-1/4,a)', 'Cmma', 'Cmmb', 'Cmme', 'Cmmm', 'Cmmm(a-1/4,b-1/4,c)', 'Cmmm(b-1/4,c-1/4,a)', 'Cmmm(c-1/4,a-1/4,b)', 'Cn11', 'F-43c', 'F-43m', 'F222', 'F23', 'F2dd', 'F2mm', 'F4132', 'F432', 'F4_132', 'Fd-3', 'Fd-3:1', 'Fd-3:2', 'Fd-3c', 'Fd-3c:1', 'Fd-3c:2', 'Fd-3m', 'Fd-3m:1', 'Fd-3m:2', 'Fd2d', 'Fdd2', 'Fddd', 'Fddd:1', 'Fddd:2', 'Fm-3', 'Fm-3(a-1/4,b-1/4,c-1/4)', 'Fm-3c', 'Fm-3c(a+1/4,b+1/4,c+1/4)', 'Fm-3m', 'Fm-3m(a-1/4,b-1/4,c-1/4)', 'Fm2m', 'Fmm2', 'Fmm2(a+1/4,b+1/4,c+1/2)', 'Fmm2(a+1/4,b,c+1/4)', 'Fmm2(a,b-1/4,c-1/4)', 'Fmm2(b+1/4,c+1/4,a+1/2)', 'Fmm2(b+1/4,c,a+1/4)', 'Fmm2(b,c-1/4,a-1/4)', 'Fmmm', 'Fmmm(a+1/2,b+1/4,c+1/4)', 'Fmmm(a+1/4,b+1/4,c)', 'Fmmm(a-1/4,b+1/2,c+1/4)', 'Fmmm(a-1/4,b-1/4,c-1/4)', 'I-1', 'I-4', 'I-42d', 'I-42m', 'I-43d', 'I-43m', 'I-4c2', 'I-4m2', 'I112', 'I112/a', 'I112/b', 'I112/m', 'I11a', 'I11b', 'I11m', 'I12/a1', 'I12/c1', 'I12/m1', 'I121', 'I1a1', 'I1c1', 'I1m1', 'I2/b11', 'I2/c11', 'I2/m11', 'I211', 'I212121', 'I213', 'I222', 'I23', 'I2_12_12_1', 'I2_13', 'I2cb', 'I2cm', 'I2mb', 'I2mm', 'I4', 'I4/m', 'I4/m(a+1/2,b,c)', 'I4/m(a+1/2,b,c-1/4)', 'I4/m(a+b+1/2,-a+b,c)', 'I4/m(a+b+1/2,-a+b,c-1/4)', 'I4/m(a+b,-a+b,c)', 'I4/m(a-1/4,b-1/4,c+1/4)', 'I4/mcm', 'I4/mcm(a+1/2,b,c)', 'I4/mcm(a+1/2,b,c+1/4)', 'I4/mcm(a+1/4,b-1/4,c+1/4)', 'I4/mcm(a+b+1/2,-a+b,c)', 'I4/mcm(a+b+1/2,-a+b,c+1/4)', 'I4/mcm(a+b,-a+b,c)', 'I4/mcm(a+b,-a+b,c+1/4)', 'I4/mcm(a,b,c+1/4)', 'I4/mcm(a-1/4,b-1/4,c+1/4)', 'I4/mmm', 'I4/mmm(a+1/2,b,c)', 'I4/mmm(a+1/2,b,c-1/4)', 'I4/mmm(a+1/4,b-1/4,c+1/4)', 'I4/mmm(a+b+1/2,-a+b,c)', 'I4/mmm(a+b+1/2,-a+b,c-1/4)', 'I4/mmm(a+b,-a+b,c)', 'I4/mmm(a-1/4,b-1/4,c+1/4)', 'I41', 'I41/a', 'I41/a:1', 'I41/a:2', 'I41/acd', 'I41/acd:1', 'I41/acd:2', 'I41/amd', 'I41/amd:1', 'I41/amd:2', 'I4122', 'I4132', 'I41cd', 'I41md', 'I422', 'I432', 'I4_1', 'I4_1/a', 'I4_1/acd', 'I4_1/amd', 'I4_122', 'I4_132', 'I4_1cd', 'I4_1md', 'I4cm', 'I4mm', 'Ia-3', 'Ia-3d', 'Ib11', 'Iba2', 'Iba2(a-1/4,b-1/4,c+1/4)', 'Iba2(b-1/4,c-1/4,a+1/4)', 'Ibam', 'Ibam(a+1/4,b-1/4,c+1/4)', 'Ibam(a,b,c+1/4)', 'Ibam(b+1/4,c-1/4,a+1/4)', 'Ibam(b,c,a+1/4)', 'Ibam(c+1/4,a-1/4,b+1/4)', 'Ibam(c,a,b+1/4)', 'Ibca', 'Ibm2', 'Ibmm', 'Ic11', 'Ic2a', 'Ic2m', 'Icab', 'Icma', 'Icmm', 'Im-3', 'Im-3(a-1/4,b-1/4,c-1/4)', 'Im-3m', 'Im-3m(a-1/4,b-1/4,c-1/4)', 'Im11', 'Im2a', 'Im2m', 'Ima2', 'Ima2(-a-1/4,c-1/4,b+1/4)', 'Ima2(a-1/4,b-1/4,c+1/4)', 'Ima2(b-1/4,-a-1/4,c+1/4)', 'Ima2(b-1/4,c-1/4,a+1/4)', 'Imam', 'Imcb', 'Imcm', 'Imm2', 'Imm2(a,b-1/4,c)', 'Imm2(a-1/4,b,c+1/4)', 'Imm2(b,c-1/4,a)', 'Imm2(b-1/4,c,a+1/4)', 'Imma', 'Immb', 'Immm', 'Immm(a+1/4,b-1/4,c+1/4)', 'Immm(a,b,c-1/4)', 'Immm(a,b-1/4,c)', 'Immm(a-1/4,b,c)', 'P-1', 'P-1(-a+b+c,a-b+c,a+b-c)', 'P-3', 'P-31c', 'P-31m', 'P-3c1', 'P-3m1', 'P-4', 'P-421c', 'P-421m', 'P-42_1c', 'P-42_1m', 'P-42c', 'P-42m', 'P-43m', 'P-43n', 'P-4b2', 'P-4c2', 'P-4m2', 'P-4n2', 'P-6', 'P-62c', 'P-62m', 'P-6c2', 'P-6m2', 'P1', 'P1(-a+b+c,a-b+c,a+b-c)', 'P1(-a+c,-b,a+c)', 'P1(-a,-b+c,b+c)', 'P1(b+c,a+c,a+b)', 'P112', 'P112/a', 'P112/b', 'P112/m', 'P112/n', 'P1121', 'P1121/a', 'P1121/b', 'P1121/m', 'P1121/n', 'P11a', 'P11b', 'P11m', 'P11n', 'P12/a1', 'P12/c1', 'P12/c1(2*a+c,b,c)', 'P12/c1(a,2*b,c)', 'P12/c1(b,c,2*a+c)', 'P12/c1(c,2*a+c,b)', 'P12/m1', 'P12/m1(2*a+c,b,c)', 'P12/m1(b,c,2*a+c)', 'P12/m1(c,2*a+c,b)', 'P12/n1', 'P121', 'P121(2*a+c,b,c)', 'P121(c,2*a+c,b)', 'P121/a1', 'P121/c1', 'P121/c1(2*a+c,b,c)', 'P121/c1(2*c,2*a+c,b)', 'P121/c1(b,c,2*a+c)', 'P121/c1(c,2*a+c,b)', 'P121/m1', 'P121/m1(b,c,2*a+c)', 'P121/m1(c,2*a+c,b)', 'P121/n1', 'P1211', 'P1211(a-1/4,b,c)', 'P1211(c,2*a+c,b)', 'P12_1/c1', 'P12_1/m1', 'P12_11', 'P1a1', 'P1c1', 'P1c1(2*a+c,b,c)', 'P1c1(b,c,2*a+c)', 'P1c1(c,2*a+c,b)', 'P1m1', 'P1m1(2*a+c,b,c)', 'P1m1(b,c,2*a+c)', 'P1m1(c,2*a+c,b)', 'P1n1', 'P2/b11', 'P2/c11', 'P2/m11', 'P2/n11', 'P21/b11', 'P21/c11', 'P21/m11', 'P21/n11', 'P211', 'P2111', 'P21212', 'P212121', 'P212121(originshiftx,y,z+1/4)', 'P2122', 'P21221', 'P213', 'P21ab', 'P21am', 'P21ca', 'P21cn', 'P21ma', 'P21mn', 'P21nb', 'P21nm', 'P2212', 'P22121', 'P222', 'P2221', 'P222_1', 'P23', 'P2_12_12', 'P2_12_12_1', 'P2_13', 'P2aa', 'P2an', 'P2cb', 'P2cm', 'P2mb', 'P2mm', 'P2na', 'P2nn', 'P3', 'P31', 'P3112', 'P312', 'P3121', 'P31c', 'P31m', 'P32', 'P321', 'P3212', 'P3221', 'P3_1', 'P3_112', 'P3_121', 'P3_2', 'P3_212', 'P3_221', 'P3c1', 'P3m1', 'P4', 'P4/m', 'P4/m(a+b,-a+b+1/2,c)', 'P4/m(a+b,-a+b,c)', 'P4/mbm', 'P4/mcc', 'P4/mcc(a+b,-a+b+1/2,c)', 'P4/mcc(a+b,-a+b,c)', 'P4/mcc(a+b,-a+b,c+1/4)', 'P4/mmm', 'P4/mmm(a+b,-a+b+1/2,c)', 'P4/mmm(a+b,-a+b,c)', 'P4/mnc', 'P4/n', 'P4/n:1', 'P4/n:2', 'P4/nbm', 'P4/nbm:1', 'P4/nbm:2', 'P4/ncc', 'P4/ncc:1', 'P4/ncc:2', 'P4/nmm', 'P4/nmm:1', 'P4/nmm:2', 'P4/nnc', 'P4/nnc:1', 'P4/nnc:2', 'P41', 'P41212', 'P4122', 'P4132', 'P42', 'P42/m', 'P42/m(a+b,-a+b+1/2,c)', 'P42/m(a+b,-a+b,c)', 'P42/m(a+b,-a+b,c-1/4)', 'P42/mbc', 'P42/mcm', 'P42/mcm(a+b,-a+b+1/2,c)', 'P42/mcm(a+b,-a+b,c)', 'P42/mcm(a+b,-a+b,c+1/4)', 'P42/mmc', 'P42/mmc(a+b,-a+b+1/2,c)', 'P42/mmc(a+b,-a+b,c)', 'P42/mmc(a+b,-a+b,c-1/4)', 'P42/mnm', 'P42/n', 'P42/n:1', 'P42/n:2', 'P42/nbc', 'P42/nbc:1', 'P42/nbc:2', 'P42/ncm', 'P42/ncm:1', 'P42/ncm:2', 'P42/nmc', 'P42/nmc:1', 'P42/nmc:2', 'P42/nnm', 'P42/nnm:1', 'P42/nnm:2', 'P4212', 'P422', 'P42212', 'P4222', 'P4232', 'P42_12', 'P42bc', 'P42cm', 'P42mc', 'P42nm', 'P43', 'P432', 'P43212', 'P4322', 'P4332', 'P4_1', 'P4_122', 'P4_12_12', 'P4_132', 'P4_2', 'P4_2/m', 'P4_2/mbc', 'P4_2/mcm', 'P4_2/mmc', 'P4_2/mnm', 'P4_2/n', 'P4_2/nbc', 'P4_2/ncm', 'P4_2/nmc', 'P4_2/nnm', 'P4_222', 'P4_22_12', 'P4_232', 'P4_2bc', 'P4_2cm', 'P4_2mc', 'P4_2nm', 'P4_3', 'P4_322', 'P4_32_12', 'P4_332', 'P4bm', 'P4bm(a,b,2*c)', 'P4cc', 'P4mm', 'P4nc', 'P6', 'P6/m', 'P6/m(2*a,2*b,2*c)', 'P6/m(2*a,2*b,c)', 'P6/mcc', 'P6/mcc(2*a,2*b,c)', 'P6/mmm', 'P6/mmm(2*a,2*b,2*c)', 'P6/mmm(2*a,2*b,c)', 'P61', 'P6122', 'P62', 'P622', 'P6222', 'P63', 'P63/m', 'P63/m(2*a,2*b,c)', 'P63/mcm', 'P63/mcm(2*a,2*b,c)', 'P63/mmc', 'P63/mmc(2*a,2*b,c)', 'P6322', 'P63cm', 'P63mc', 'P64', 'P6422', 'P65', 'P6522', 'P6_1', 'P6_122', 'P6_2', 'P6_222', 'P6_3', 'P6_3/m', 'P6_3/mcm', 'P6_3/mmc', 'P6_322', 'P6_3cm', 'P6_3mc', 'P6_4', 'P6_422', 'P6_5', 'P6_522', 'P6cc', 'P6mm', 'Pa-3', 'Pb11', 'Pb21a', 'Pb21m', 'Pb2b', 'Pb2n', 'Pba2', 'Pbaa', 'Pbab', 'Pbam', 'Pban', 'Pban:1', 'Pban:2', 'Pbc21', 'Pbca', 'Pbcb', 'Pbcm', 'Pbcn', 'Pbm2', 'Pbma', 'Pbmb', 'Pbmm', 'Pbmn', 'Pbn21', 'Pbna', 'Pbnb', 'Pbnm', 'Pbnn', 'Pc11', 'Pc21b', 'Pc21n', 'Pc2a', 'Pc2m', 'Pca21', 'Pca2_1', 'Pcaa', 'Pcab', 'Pcam', 'Pcan', 'Pcc2', 'Pcca', 'Pccb', 'Pccm', 'Pccn', 'Pcm21', 'Pcma', 'Pcmb', 'Pcmm', 'Pcmn', 'Pcn2', 'Pcna', 'Pcna:1', 'Pcna:2', 'Pcnb', 'Pcnm', 'Pcnn', 'Pm-3', 'Pm-3m', 'Pm-3n', 'Pm11', 'Pm21b', 'Pm21n', 'Pm2a', 'Pm2m', 'Pma2', 'Pmaa', 'Pmab', 'Pmam', 'Pman', 'Pmc21', 'Pmc21(2*a,b,c)', 'Pmc2_1', 'Pmca', 'Pmcb', 'Pmcm', 'Pmcn', 'Pmm2', 'Pmma', 'Pmma(2*b+1/4,c,a-1/3)', 'Pmma(2*b,c,a)', 'Pmmb', 'Pmmm', 'Pmmm(2*a,2*b,c)', 'Pmmn', 'Pmmn:1', 'Pmmn:2', 'Pmn21', 'Pmn2_1', 'Pmna', 'Pmnb', 'Pmnm', 'Pmnm:1', 'Pmnm:2', 'Pmnn', 'Pn-3', 'Pn-3:1', 'Pn-3:2', 'Pn-3m', 'Pn-3m:1', 'Pn-3m:2', 'Pn-3n', 'Pn-3n:1', 'Pn-3n:2', 'Pn11', 'Pn21a', 'Pn21m', 'Pn2b', 'Pn2n', 'Pna21', 'Pna2_1', 'Pnaa', 'Pnab', 'Pnam', 'Pnan', 'Pnc2', 'Pnca', 'Pncb', 'Pncb:1', 'Pncb:2', 'Pncm', 'Pncn', 'Pnm21', 'Pnma', 'Pnma(c,a-1/4,b)', 'Pnmb', 'Pnmm', 'Pnmm:1', 'Pnmm:2', 'Pnmn', 'Pnn2', 'Pnna', 'Pnnb', 'Pnnm', 'Pnnn', 'Pnnn:1', 'Pnnn:2', 'R-3', 'R-3:H', 'R-3:R', 'R-3c', 'R-3c:H', 'R-3c:R', 'R-3m', 'R-3m:H', 'R-3m:R', 'R12/c1', 'R3', 'R32', 'R32:H', 'R32:R', 'R3:H', 'R3:R', 'R3c', 'R3c:H', 'R3c:R', 'R3m', 'R3m:H', 'R3m:R'}[source]

SYMM_OPS = [{'hall': ' P 1', 'hermann_mauguin': 'P1', 'hermann_mauguin_u': 'P1', 'ncsym': ['x,y,z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'P1', 'symops': ['x,y,z'], 'universal_h_m': 'P1'}, {'hall': '-P 1', 'hermann_mauguin': 'P-1', 'hermann_mauguin_u': 'P-1', 'ncsym': ['x,y,z', '-x,-y,-z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'Ci^1', 'short_h_m': 'P-1', 'symops': ['x,y,z', '-x,-y,-z'], 'universal_h_m': 'P-1'}, {'hall': ' P 2y', 'hermann_mauguin': 'P121', 'hermann_mauguin_u': 'P121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 3, 'point_group': '2', 'schoenflies': 'C2^1', 'short_h_m': 'P2', 'symops': ['x,y,z', '-x,y,-z'], 'universal_h_m': 'P121'}, {'hall': ' P 2', 'hermann_mauguin': 'P112', 'hermann_mauguin_u': 'P112', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 3, 'point_group': '2', 'schoenflies': 'C2^1', 'short_h_m': 'P2', 'symops': ['x,y,z', '-x,-y,z'], 'universal_h_m': 'P112'}, {'hall': ' P 2x', 'hermann_mauguin': 'P211', 'hermann_mauguin_u': 'P211', 'ncsym': ['x,y,z', 'x,-y,-z'], 'number': 3, 'point_group': '2', 'schoenflies': 'C2^1', 'short_h_m': 'P2', 'symops': ['x,y,z', 'x,-y,-z'], 'universal_h_m': 'P211'}, {'hall': ' P 2yb', 'hermann_mauguin': 'P1211', 'hermann_mauguin_u': 'P12_11', 'ncsym': ['x,y,z', '-x,y+1/2,-z'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'P2_1', 'symops': ['x,y,z', '-x,y+1/2,-z'], 'universal_h_m': 'P1211'}, {'hall': ' P 2c', 'hermann_mauguin': 'P1121', 'hermann_mauguin_u': 'P112_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'P2_1', 'symops': ['x,y,z', '-x,-y,z+1/2'], 'universal_h_m': 'P1121'}, {'hall': ' P 2xa', 'hermann_mauguin': 'P2111', 'hermann_mauguin_u': 'P2_111', 'ncsym': ['x,y,z', 'x+1/2,-y,-z'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'P2_1', 'symops': ['x,y,z', 'x+1/2,-y,-z'], 'universal_h_m': 'P2111'}, {'hall': ' C 2y', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,y,-z', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'C121'}, {'hall': ' A 2y', 'hermann_mauguin': 'A121', 'hermann_mauguin_u': 'A121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'A2', 'symops': ['x,y,z', '-x,y,-z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'A121'}, {'hall': ' I 2y', 'hermann_mauguin': 'I121', 'hermann_mauguin_u': 'I121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'I2', 'symops': ['x,y,z', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'I121'}, {'hall': ' A 2', 'hermann_mauguin': 'A112', 'hermann_mauguin_u': 'A112', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'A2', 'symops': ['x,y,z', '-x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2'], 'universal_h_m': 'A112'}, {'hall': ' B 2', 'hermann_mauguin': 'B112', 'hermann_mauguin_u': 'B112', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'B2', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2'], 'universal_h_m': 'B112'}, {'hall': ' I 2', 'hermann_mauguin': 'I112', 'hermann_mauguin_u': 'I112', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'I2', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'I112'}, {'hall': ' B 2x', 'hermann_mauguin': 'B211', 'hermann_mauguin_u': 'B211', 'ncsym': ['x,y,z', 'x,-y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'B2', 'symops': ['x,y,z', 'x,-y,-z', 'x+1/2,y,z+1/2', 'x+1/2,-y,-z+1/2'], 'universal_h_m': 'B211'}, {'hall': ' C 2x', 'hermann_mauguin': 'C211', 'hermann_mauguin_u': 'C211', 'ncsym': ['x,y,z', 'x,-y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', 'x,-y,-z', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,-z'], 'universal_h_m': 'C211'}, {'hall': ' I 2x', 'hermann_mauguin': 'I211', 'hermann_mauguin_u': 'I211', 'ncsym': ['x,y,z', 'x,-y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'I2', 'symops': ['x,y,z', 'x,-y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2'], 'universal_h_m': 'I211'}, {'hall': ' P -2y', 'hermann_mauguin': 'P1m1', 'hermann_mauguin_u': 'P1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', 'x,-y,z'], 'universal_h_m': 'P1m1'}, {'hall': ' P -2', 'hermann_mauguin': 'P11m', 'hermann_mauguin_u': 'P11m', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', 'x,y,-z'], 'universal_h_m': 'P11m'}, {'hall': ' P -2x', 'hermann_mauguin': 'Pm11', 'hermann_mauguin_u': 'Pm11', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', '-x,y,z'], 'universal_h_m': 'Pm11'}, {'hall': ' P -2yc', 'hermann_mauguin': 'P1c1', 'hermann_mauguin_u': 'P1c1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pc', 'symops': ['x,y,z', 'x,-y,z+1/2'], 'universal_h_m': 'P1c1'}, {'hall': ' P -2yac', 'hermann_mauguin': 'P1n1', 'hermann_mauguin_u': 'P1n1', 'ncsym': ['x,y,z', 'x+1/2,-y,z+1/2'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pn', 'symops': ['x,y,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P1n1'}, {'hall': ' P -2ya', 'hermann_mauguin': 'P1a1', 'hermann_mauguin_u': 'P1a1', 'ncsym': ['x,y,z', 'x+1/2,-y,z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pa', 'symops': ['x,y,z', 'x+1/2,-y,z'], 'universal_h_m': 'P1a1'}, {'hall': ' P -2a', 'hermann_mauguin': 'P11a', 'hermann_mauguin_u': 'P11a', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pa', 'symops': ['x,y,z', 'x+1/2,y,-z'], 'universal_h_m': 'P11a'}, {'hall': ' P -2ab', 'hermann_mauguin': 'P11n', 'hermann_mauguin_u': 'P11n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pn', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'P11n'}, {'hall': ' P -2b', 'hermann_mauguin': 'P11b', 'hermann_mauguin_u': 'P11b', 'ncsym': ['x,y,z', 'x,y+1/2,-z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pb', 'symops': ['x,y,z', 'x,y+1/2,-z'], 'universal_h_m': 'P11b'}, {'hall': ' P -2xb', 'hermann_mauguin': 'Pb11', 'hermann_mauguin_u': 'Pb11', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pb', 'symops': ['x,y,z', '-x,y+1/2,z'], 'universal_h_m': 'Pb11'}, {'hall': ' P -2xbc', 'hermann_mauguin': 'Pn11', 'hermann_mauguin_u': 'Pn11', 'ncsym': ['x,y,z', '-x,y+1/2,z+1/2'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pn', 'symops': ['x,y,z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Pn11'}, {'hall': ' P -2xc', 'hermann_mauguin': 'Pc11', 'hermann_mauguin_u': 'Pc11', 'ncsym': ['x,y,z', '-x,y,z+1/2'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pc', 'symops': ['x,y,z', '-x,y,z+1/2'], 'universal_h_m': 'Pc11'}, {'hall': ' C -2y', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'C1m1'}, {'hall': ' A -2y', 'hermann_mauguin': 'A1m1', 'hermann_mauguin_u': 'A1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Am', 'symops': ['x,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'A1m1'}, {'hall': ' I -2y', 'hermann_mauguin': 'I1m1', 'hermann_mauguin_u': 'I1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Im', 'symops': ['x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'I1m1'}, {'hall': ' A -2', 'hermann_mauguin': 'A11m', 'hermann_mauguin_u': 'A11m', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Am', 'symops': ['x,y,z', 'x,y,-z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'A11m'}, {'hall': ' B -2', 'hermann_mauguin': 'B11m', 'hermann_mauguin_u': 'B11m', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Bm', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2'], 'universal_h_m': 'B11m'}, {'hall': ' I -2', 'hermann_mauguin': 'I11m', 'hermann_mauguin_u': 'I11m', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Im', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'I11m'}, {'hall': ' B -2x', 'hermann_mauguin': 'Bm11', 'hermann_mauguin_u': 'Bm11', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Bm', 'symops': ['x,y,z', '-x,y,z', 'x+1/2,y,z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'Bm11'}, {'hall': ' C -2x', 'hermann_mauguin': 'Cm11', 'hermann_mauguin_u': 'Cm11', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x,y,z', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'Cm11'}, {'hall': ' I -2x', 'hermann_mauguin': 'Im11', 'hermann_mauguin_u': 'Im11', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Im', 'symops': ['x,y,z', '-x,y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Im11'}, {'hall': ' C -2yc', 'hermann_mauguin': 'C1c1', 'hermann_mauguin_u': 'C1c1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Cc', 'symops': ['x,y,z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'C1c1'}, {'hall': ' A -2yab', 'hermann_mauguin': 'A1n1', 'hermann_mauguin_u': 'A1n1', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'An', 'symops': ['x,y,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', 'x+1/2,-y+1,z+1/2'], 'universal_h_m': 'A1n1'}, {'hall': ' I -2ya', 'hermann_mauguin': 'I1a1', 'hermann_mauguin_u': 'I1a1', 'ncsym': ['x,y,z', 'x+1/2,-y,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ia', 'symops': ['x,y,z', 'x+1/2,-y,z', 'x+1/2,y+1/2,z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'I1a1'}, {'hall': ' A -2ya', 'hermann_mauguin': 'A1a1', 'hermann_mauguin_u': 'A1a1', 'ncsym': ['x,y,z', 'x+1/2,-y,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Aa', 'symops': ['x,y,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'A1a1'}, {'hall': ' C -2yac', 'hermann_mauguin': 'C1n1', 'hermann_mauguin_u': 'C1n1', 'ncsym': ['x,y,z', 'x+1/2,-y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Cn', 'symops': ['x,y,z', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'C1n1'}, {'hall': ' I -2yc', 'hermann_mauguin': 'I1c1', 'hermann_mauguin_u': 'I1c1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ic', 'symops': ['x,y,z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1'], 'universal_h_m': 'I1c1'}, {'hall': ' A -2a', 'hermann_mauguin': 'A11a', 'hermann_mauguin_u': 'A11a', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Aa', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'A11a'}, {'hall': ' B -2ab', 'hermann_mauguin': 'B11n', 'hermann_mauguin_u': 'B11n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Bn', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', 'x+1/2,y,z+1/2', 'x+1,y+1/2,-z+1/2'], 'universal_h_m': 'B11n'}, {'hall': ' I -2b', 'hermann_mauguin': 'I11b', 'hermann_mauguin_u': 'I11b', 'ncsym': ['x,y,z', 'x,y+1/2,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ib', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1,-z+1/2'], 'universal_h_m': 'I11b'}, {'hall': ' B -2b', 'hermann_mauguin': 'B11b', 'hermann_mauguin_u': 'B11b', 'ncsym': ['x,y,z', 'x,y+1/2,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Bb', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'B11b'}, {'hall': ' A -2ab', 'hermann_mauguin': 'A11n', 'hermann_mauguin_u': 'A11n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'An', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', 'x,y+1/2,z+1/2', 'x+1/2,y+1,-z+1/2'], 'universal_h_m': 'A11n'}, {'hall': ' I -2a', 'hermann_mauguin': 'I11a', 'hermann_mauguin_u': 'I11a', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ia', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1,y+1/2,-z+1/2'], 'universal_h_m': 'I11a'}, {'hall': ' B -2xb', 'hermann_mauguin': 'Bb11', 'hermann_mauguin_u': 'Bb11', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Bb', 'symops': ['x,y,z', '-x,y+1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Bb11'}, {'hall': ' C -2xac', 'hermann_mauguin': 'Cn11', 'hermann_mauguin_u': 'Cn11', 'ncsym': ['x,y,z', '-x+1/2,y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Cn', 'symops': ['x,y,z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x+1,y+1/2,z+1/2'], 'universal_h_m': 'Cn11'}, {'hall': ' I -2xc', 'hermann_mauguin': 'Ic11', 'hermann_mauguin_u': 'Ic11', 'ncsym': ['x,y,z', '-x,y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ic', 'symops': ['x,y,z', '-x,y,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,z+1'], 'universal_h_m': 'Ic11'}, {'hall': ' C -2xc', 'hermann_mauguin': 'Cc11', 'hermann_mauguin_u': 'Cc11', 'ncsym': ['x,y,z', '-x,y,z+1/2'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Cc', 'symops': ['x,y,z', '-x,y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Cc11'}, {'hall': ' B -2xab', 'hermann_mauguin': 'Bn11', 'hermann_mauguin_u': 'Bn11', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Bn', 'symops': ['x,y,z', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x+1,y+1/2,z+1/2'], 'universal_h_m': 'Bn11'}, {'hall': ' I -2xb', 'hermann_mauguin': 'Ib11', 'hermann_mauguin_u': 'Ib11', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Ib', 'symops': ['x,y,z', '-x,y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1,z+1/2'], 'universal_h_m': 'Ib11'}, {'hall': '-P 2y', 'hermann_mauguin': 'P12/m1', 'hermann_mauguin_u': 'P12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'universal_h_m': 'P12/m1'}, {'hall': '-P 2', 'hermann_mauguin': 'P112/m', 'hermann_mauguin_u': 'P112/m', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'universal_h_m': 'P112/m'}, {'hall': '-P 2x', 'hermann_mauguin': 'P2/m11', 'hermann_mauguin_u': 'P2/m11', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'universal_h_m': 'P2/m11'}, {'hall': '-P 2yb', 'hermann_mauguin': 'P121/m1', 'hermann_mauguin_u': 'P12_1/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y-1/2,z'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'P2_1/m', 'symops': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y-1/2,z'], 'universal_h_m': 'P121/m1'}, {'hall': '-P 2c', 'hermann_mauguin': 'P1121/m', 'hermann_mauguin_u': 'P112_1/m', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z-1/2'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'P2_1/m', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z-1/2'], 'universal_h_m': 'P1121/m'}, {'hall': '-P 2xa', 'hermann_mauguin': 'P21/m11', 'hermann_mauguin_u': 'P2_1/m11', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x-1/2,y,z'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'P2_1/m', 'symops': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x-1/2,y,z'], 'universal_h_m': 'P21/m11'}, {'hall': '-C 2y', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'C12/m1'}, {'hall': '-A 2y', 'hermann_mauguin': 'A12/m1', 'hermann_mauguin_u': 'A12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'A2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'A12/m1'}, {'hall': '-I 2y', 'hermann_mauguin': 'I12/m1', 'hermann_mauguin_u': 'I12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'I2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'I12/m1'}, {'hall': '-A 2', 'hermann_mauguin': 'A112/m', 'hermann_mauguin_u': 'A112/m', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'A2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'A112/m'}, {'hall': '-B 2', 'hermann_mauguin': 'B112/m', 'hermann_mauguin_u': 'B112/m', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'B2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2'], 'universal_h_m': 'B112/m'}, {'hall': '-I 2', 'hermann_mauguin': 'I112/m', 'hermann_mauguin_u': 'I112/m', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'I2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'I112/m'}, {'hall': '-B 2x', 'hermann_mauguin': 'B2/m11', 'hermann_mauguin_u': 'B2/m11', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'B2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z', 'x+1/2,y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'B2/m11'}, {'hall': '-C 2x', 'hermann_mauguin': 'C2/m11', 'hermann_mauguin_u': 'C2/m11', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'C2/m11'}, {'hall': '-I 2x', 'hermann_mauguin': 'I2/m11', 'hermann_mauguin_u': 'I2/m11', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'I2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'I2/m11'}, {'hall': '-P 2yc', 'hermann_mauguin': 'P12/c1', 'hermann_mauguin_u': 'P12/c1', 'ncsym': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2'], 'universal_h_m': 'P12/c1'}, {'hall': '-P 2yac', 'hermann_mauguin': 'P12/n1', 'hermann_mauguin_u': 'P12/n1', 'ncsym': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,-y,z-1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/n', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'P12/n1'}, {'hall': '-P 2ya', 'hermann_mauguin': 'P12/a1', 'hermann_mauguin_u': 'P12/a1', 'ncsym': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/a', 'symops': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z'], 'universal_h_m': 'P12/a1'}, {'hall': '-P 2a', 'hermann_mauguin': 'P112/a', 'hermann_mauguin_u': 'P112/a', 'ncsym': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/a', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z'], 'universal_h_m': 'P112/a'}, {'hall': '-P 2ab', 'hermann_mauguin': 'P112/n', 'hermann_mauguin_u': 'P112/n', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/n', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z'], 'universal_h_m': 'P112/n'}, {'hall': '-P 2b', 'hermann_mauguin': 'P112/b', 'hermann_mauguin_u': 'P112/b', 'ncsym': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/b', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z'], 'universal_h_m': 'P112/b'}, {'hall': '-P 2xb', 'hermann_mauguin': 'P2/b11', 'hermann_mauguin_u': 'P2/b11', 'ncsym': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/b', 'symops': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z'], 'universal_h_m': 'P2/b11'}, {'hall': '-P 2xbc', 'hermann_mauguin': 'P2/n11', 'hermann_mauguin_u': 'P2/n11', 'ncsym': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x,-y,-z', '-x,y-1/2,z-1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/n', 'symops': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x,-y,-z', '-x,y-1/2,z-1/2'], 'universal_h_m': 'P2/n11'}, {'hall': '-P 2xc', 'hermann_mauguin': 'P2/c11', 'hermann_mauguin_u': 'P2/c11', 'ncsym': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2'], 'universal_h_m': 'P2/c11'}, {'hall': '-P 2ybc', 'hermann_mauguin': 'P121/c1', 'hermann_mauguin_u': 'P12_1/c1', 'ncsym': ['x,y,z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,-y-1/2,z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'P121/c1'}, {'hall': '-P 2yn', 'hermann_mauguin': 'P121/n1', 'hermann_mauguin_u': 'P12_1/n1', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,-y-1/2,z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/n', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'P121/n1'}, {'hall': '-P 2yab', 'hermann_mauguin': 'P121/a1', 'hermann_mauguin_u': 'P12_1/a1', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,-y-1/2,z'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/a', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'P121/a1'}, {'hall': '-P 2ac', 'hermann_mauguin': 'P1121/a', 'hermann_mauguin_u': 'P112_1/a', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/a', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2'], 'universal_h_m': 'P1121/a'}, {'hall': '-P 2n', 'hermann_mauguin': 'P1121/n', 'hermann_mauguin_u': 'P112_1/n', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/n', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2'], 'universal_h_m': 'P1121/n'}, {'hall': '-P 2bc', 'hermann_mauguin': 'P1121/b', 'hermann_mauguin_u': 'P112_1/b', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/b', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2'], 'universal_h_m': 'P1121/b'}, {'hall': '-P 2xab', 'hermann_mauguin': 'P21/b11', 'hermann_mauguin_u': 'P2_1/b11', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x-1/2,y-1/2,z'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/b', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x-1/2,y-1/2,z'], 'universal_h_m': 'P21/b11'}, {'hall': '-P 2xn', 'hermann_mauguin': 'P21/n11', 'hermann_mauguin_u': 'P2_1/n11', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z', '-x-1/2,y-1/2,z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/n', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z', '-x-1/2,y-1/2,z-1/2'], 'universal_h_m': 'P21/n11'}, {'hall': '-P 2xac', 'hermann_mauguin': 'P21/c11', 'hermann_mauguin_u': 'P2_1/c11', 'ncsym': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x,-y,-z', '-x-1/2,y,z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x,-y,-z', '-x-1/2,y,z-1/2'], 'universal_h_m': 'P21/c11'}, {'hall': '-C 2yc', 'hermann_mauguin': 'C12/c1', 'hermann_mauguin_u': 'C12/c1', 'ncsym': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'C2/c', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z-1/2'], 'universal_h_m': 'C12/c1'}, {'hall': '-A 2yab', 'hermann_mauguin': 'A12/n1', 'hermann_mauguin_u': 'A12/n1', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,-y-1/2,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'A2/n', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,-y-1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,-y,z+1/2'], 'universal_h_m': 'A12/n1'}, {'hall': '-I 2ya', 'hermann_mauguin': 'I12/a1', 'hermann_mauguin_u': 'I12/a1', 'ncsym': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/a', 'symops': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'I12/a1'}, {'hall': '-A 2ya', 'hermann_mauguin': 'A12/a1', 'hermann_mauguin_u': 'A12/a1', 'ncsym': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'A2/a', 'symops': ['x,y,z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,-y+1/2,z+1/2'], 'universal_h_m': 'A12/a1'}, {'hall': '-C 2yac', 'hermann_mauguin': 'C12/n1', 'hermann_mauguin_u': 'C12/n1', 'ncsym': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,-y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'C2/n', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,-y+1/2,z-1/2'], 'universal_h_m': 'C12/n1'}, {'hall': '-I 2yc', 'hermann_mauguin': 'I12/c1', 'hermann_mauguin_u': 'I12/c1', 'ncsym': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/c', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z-1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'I12/c1'}, {'hall': '-A 2a', 'hermann_mauguin': 'A112/a', 'hermann_mauguin_u': 'A112/a', 'ncsym': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'A2/a', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y+1/2,-z+1/2'], 'universal_h_m': 'A112/a'}, {'hall': '-B 2ab', 'hermann_mauguin': 'B112/n', 'hermann_mauguin_u': 'B112/n', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'B2/n', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z', 'x+1/2,y,z+1/2', '-x+1,-y+1/2,z+1/2', '-x+1/2,-y,-z+1/2', 'x,y-1/2,-z+1/2'], 'universal_h_m': 'B112/n'}, {'hall': '-I 2b', 'hermann_mauguin': 'I112/b', 'hermann_mauguin_u': 'I112/b', 'ncsym': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/b', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2'], 'universal_h_m': 'I112/b'}, {'hall': '-B 2b', 'hermann_mauguin': 'B112/b', 'hermann_mauguin_u': 'B112/b', 'ncsym': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'B2/b', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,-y,-z', 'x,y-1/2,-z', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y-1/2,-z+1/2'], 'universal_h_m': 'B112/b'}, {'hall': '-A 2ab', 'hermann_mauguin': 'A112/n', 'hermann_mauguin_u': 'A112/n', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'A2/n', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x-1/2,y-1/2,-z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y,-z+1/2'], 'universal_h_m': 'A112/n'}, {'hall': '-I 2a', 'hermann_mauguin': 'I112/a', 'hermann_mauguin_u': 'I112/a', 'ncsym': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/a', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x-1/2,y,-z', 'x+1/2,y+1/2,z+1/2', '-x+1,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'I112/a'}, {'hall': '-B 2xb', 'hermann_mauguin': 'B2/b11', 'hermann_mauguin_u': 'B2/b11', 'ncsym': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'B2/b', 'symops': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z', 'x+1/2,y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+1/2,y-1/2,z+1/2'], 'universal_h_m': 'B2/b11'}, {'hall': '-C 2xac', 'hermann_mauguin': 'C2/n11', 'hermann_mauguin_u': 'C2/n11', 'ncsym': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x,-y,-z', '-x-1/2,y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'C2/n', 'symops': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x,-y,-z', '-x-1/2,y,z-1/2', 'x+1/2,y+1/2,z', 'x+1,-y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', '-x,y+1/2,z-1/2'], 'universal_h_m': 'C2/n11'}, {'hall': '-I 2xc', 'hermann_mauguin': 'I2/c11', 'hermann_mauguin_u': 'I2/c11', 'ncsym': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/c', 'symops': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,z'], 'universal_h_m': 'I2/c11'}, {'hall': '-C 2xc', 'hermann_mauguin': 'C2/c11', 'hermann_mauguin_u': 'C2/c11', 'ncsym': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'C2/c', 'symops': ['x,y,z', 'x,-y,-z+1/2', '-x,-y,-z', '-x,y,z-1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,z-1/2'], 'universal_h_m': 'C2/c11'}, {'hall': '-B 2xab', 'hermann_mauguin': 'B2/n11', 'hermann_mauguin_u': 'B2/n11', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x-1/2,y-1/2,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'B2/n', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x-1/2,y-1/2,z', 'x+1/2,y,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', '-x,y-1/2,z+1/2'], 'universal_h_m': 'B2/n11'}, {'hall': '-I 2xb', 'hermann_mauguin': 'I2/b11', 'hermann_mauguin_u': 'I2/b11', 'ncsym': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'I2/b', 'symops': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y-1/2,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'I2/b11'}, {'hall': ' P 2 2', 'hermann_mauguin': 'P222', 'hermann_mauguin_u': 'P222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 16, 'point_group': '222', 'schoenflies': 'D2^1', 'short_h_m': 'P222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'universal_h_m': 'P222'}, {'hall': ' P 2c 2', 'hermann_mauguin': 'P2221', 'hermann_mauguin_u': 'P222_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2'], 'number': 17, 'point_group': '222', 'schoenflies': 'D2^2', 'short_h_m': 'P222_1', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2'], 'universal_h_m': 'P2221'}, {'hall': ' P 2a 2a', 'hermann_mauguin': 'P2122', 'hermann_mauguin_u': 'P2_122', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z'], 'number': 17, 'point_group': '222', 'schoenflies': 'D2^2', 'short_h_m': 'P2_122', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z'], 'universal_h_m': 'P2122'}, {'hall': ' P 2 2b', 'hermann_mauguin': 'P2212', 'hermann_mauguin_u': 'P22_12', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z'], 'number': 17, 'point_group': '222', 'schoenflies': 'D2^2', 'short_h_m': 'P22_12', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z'], 'universal_h_m': 'P2212'}, {'hall': ' P 2 2ab', 'hermann_mauguin': 'P21212', 'hermann_mauguin_u': 'P2_12_12', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z'], 'number': 18, 'point_group': '222', 'schoenflies': 'D2^3', 'short_h_m': 'P2_12_12', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'P21212'}, {'hall': ' P 2bc 2', 'hermann_mauguin': 'P22121', 'hermann_mauguin_u': 'P22_12_1', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2'], 'number': 18, 'point_group': '222', 'schoenflies': 'D2^3', 'short_h_m': 'P22_12_1', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'P22121'}, {'hall': ' P 2ac 2ac', 'hermann_mauguin': 'P21221', 'hermann_mauguin_u': 'P2_122_1', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z'], 'number': 18, 'point_group': '222', 'schoenflies': 'D2^3', 'short_h_m': 'P2_122_1', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z'], 'universal_h_m': 'P21221'}, {'hall': ' P 2ac 2ab', 'hermann_mauguin': 'P212121', 'hermann_mauguin_u': 'P2_12_12_1', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2'], 'number': 19, 'point_group': '222', 'schoenflies': 'D2^4', 'short_h_m': 'P2_12_12_1', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'P212121'}, {'hall': ' C 2c 2', 'hermann_mauguin': 'C2221', 'hermann_mauguin_u': 'C222_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2'], 'number': 20, 'point_group': '222', 'schoenflies': 'D2^5', 'short_h_m': 'C222_1', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'C2221'}, {'hall': ' A 2a 2a', 'hermann_mauguin': 'A2122', 'hermann_mauguin_u': 'A2_122', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z'], 'number': 20, 'point_group': '222', 'schoenflies': 'D2^5', 'short_h_m': 'A2_122', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'A2122'}, {'hall': ' B 2 2b', 'hermann_mauguin': 'B2212', 'hermann_mauguin_u': 'B22_12', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z'], 'number': 20, 'point_group': '222', 'schoenflies': 'D2^5', 'short_h_m': 'B22_12', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'B2212'}, {'hall': ' C 2 2', 'hermann_mauguin': 'C222', 'hermann_mauguin_u': 'C222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 21, 'point_group': '222', 'schoenflies': 'D2^6', 'short_h_m': 'C222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'C222'}, {'hall': ' A 2 2', 'hermann_mauguin': 'A222', 'hermann_mauguin_u': 'A222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 21, 'point_group': '222', 'schoenflies': 'D2^6', 'short_h_m': 'A222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'A222'}, {'hall': ' B 2 2', 'hermann_mauguin': 'B222', 'hermann_mauguin_u': 'B222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 21, 'point_group': '222', 'schoenflies': 'D2^6', 'short_h_m': 'B222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2'], 'universal_h_m': 'B222'}, {'hall': ' F 2 2', 'hermann_mauguin': 'F222', 'hermann_mauguin_u': 'F222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 22, 'point_group': '222', 'schoenflies': 'D2^7', 'short_h_m': 'F222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'F222'}, {'hall': ' I 2 2', 'hermann_mauguin': 'I222', 'hermann_mauguin_u': 'I222', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z'], 'number': 23, 'point_group': '222', 'schoenflies': 'D2^8', 'short_h_m': 'I222', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'I222'}, {'hall': ' I 2b 2c', 'hermann_mauguin': 'I212121', 'hermann_mauguin_u': 'I2_12_12_1', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2'], 'number': 24, 'point_group': '222', 'schoenflies': 'D2^9', 'short_h_m': 'I2_12_12_1', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1,-z+1'], 'universal_h_m': 'I212121'}, {'hall': ' P 2 -2', 'hermann_mauguin': 'Pmm2', 'hermann_mauguin_u': 'Pmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 25, 'point_group': 'mm2', 'schoenflies': 'C2v^1', 'short_h_m': 'Pmm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'universal_h_m': 'Pmm2'}, {'hall': ' P -2 2', 'hermann_mauguin': 'P2mm', 'hermann_mauguin_u': 'P2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 25, 'point_group': 'mm2', 'schoenflies': 'C2v^1', 'short_h_m': 'P2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'universal_h_m': 'P2mm'}, {'hall': ' P -2 -2', 'hermann_mauguin': 'Pm2m', 'hermann_mauguin_u': 'Pm2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 25, 'point_group': 'mm2', 'schoenflies': 'C2v^1', 'short_h_m': 'Pm2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'universal_h_m': 'Pm2m'}, {'hall': ' P 2c -2', 'hermann_mauguin': 'Pmc21', 'hermann_mauguin_u': 'Pmc2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'Pmc2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'universal_h_m': 'Pmc21'}, {'hall': ' P 2c -2c', 'hermann_mauguin': 'Pcm21', 'hermann_mauguin_u': 'Pcm2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'Pcm2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'universal_h_m': 'Pcm21'}, {'hall': ' P -2a 2a', 'hermann_mauguin': 'P21ma', 'hermann_mauguin_u': 'P2_1ma', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,-y,-z', 'x,-y,z'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'P2_1ma', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,-y,-z', 'x,-y,z'], 'universal_h_m': 'P21ma'}, {'hall': ' P -2 2a', 'hermann_mauguin': 'P21am', 'hermann_mauguin_u': 'P2_1am', 'ncsym': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z', 'x+1/2,-y,z'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'P2_1am', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z', 'x+1/2,-y,z'], 'universal_h_m': 'P21am'}, {'hall': ' P -2 -2b', 'hermann_mauguin': 'Pb21m', 'hermann_mauguin_u': 'Pb2_1m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'Pb2_1m', 'symops': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'universal_h_m': 'Pb21m'}, {'hall': ' P -2b -2', 'hermann_mauguin': 'Pm21b', 'hermann_mauguin_u': 'Pm2_1b', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'Pm2_1b', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'universal_h_m': 'Pm21b'}, {'hall': ' P 2 -2c', 'hermann_mauguin': 'Pcc2', 'hermann_mauguin_u': 'Pcc2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'number': 27, 'point_group': 'mm2', 'schoenflies': 'C2v^3', 'short_h_m': 'Pcc2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Pcc2'}, {'hall': ' P -2a 2', 'hermann_mauguin': 'P2aa', 'hermann_mauguin_u': 'P2aa', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'number': 27, 'point_group': 'mm2', 'schoenflies': 'C2v^3', 'short_h_m': 'P2aa', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'universal_h_m': 'P2aa'}, {'hall': ' P -2b -2b', 'hermann_mauguin': 'Pb2b', 'hermann_mauguin_u': 'Pb2b', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'number': 27, 'point_group': 'mm2', 'schoenflies': 'C2v^3', 'short_h_m': 'Pb2b', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'universal_h_m': 'Pb2b'}, {'hall': ' P 2 -2a', 'hermann_mauguin': 'Pma2', 'hermann_mauguin_u': 'Pma2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'Pma2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'universal_h_m': 'Pma2'}, {'hall': ' P 2 -2b', 'hermann_mauguin': 'Pbm2', 'hermann_mauguin_u': 'Pbm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'Pbm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z'], 'universal_h_m': 'Pbm2'}, {'hall': ' P -2b 2', 'hermann_mauguin': 'P2mb', 'hermann_mauguin_u': 'P2mb', 'ncsym': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'P2mb', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z'], 'universal_h_m': 'P2mb'}, {'hall': ' P -2c 2', 'hermann_mauguin': 'P2cm', 'hermann_mauguin_u': 'P2cm', 'ncsym': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'P2cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2'], 'universal_h_m': 'P2cm'}, {'hall': ' P -2c -2c', 'hermann_mauguin': 'Pc2m', 'hermann_mauguin_u': 'Pc2m', 'ncsym': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'Pc2m', 'symops': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z'], 'universal_h_m': 'Pc2m'}, {'hall': ' P -2a -2a', 'hermann_mauguin': 'Pm2a', 'hermann_mauguin_u': 'Pm2a', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z'], 'number': 28, 'point_group': 'mm2', 'schoenflies': 'C2v^4', 'short_h_m': 'Pm2a', 'symops': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z'], 'universal_h_m': 'Pm2a'}, {'hall': ' P 2c -2ac', 'hermann_mauguin': 'Pca21', 'hermann_mauguin_u': 'Pca2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'Pca2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'universal_h_m': 'Pca21'}, {'hall': ' P 2c -2b', 'hermann_mauguin': 'Pbc21', 'hermann_mauguin_u': 'Pbc2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y+1/2,z', 'x,-y+1/2,z+1/2'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'Pbc2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,y+1/2,z', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Pbc21'}, {'hall': ' P -2b 2a', 'hermann_mauguin': 'P21ab', 'hermann_mauguin_u': 'P2_1ab', 'ncsym': ['x,y,z', 'x,y+1/2,-z', 'x+1/2,-y,-z', 'x+1/2,-y+1/2,z'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'P2_1ab', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x+1/2,-y,-z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P21ab'}, {'hall': ' P -2ac 2a', 'hermann_mauguin': 'P21ca', 'hermann_mauguin_u': 'P2_1ca', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', 'x+1/2,-y,-z', 'x,-y,z+1/2'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'P2_1ca', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', 'x+1/2,-y,-z', 'x,-y,z+1/2'], 'universal_h_m': 'P21ca'}, {'hall': ' P -2bc -2c', 'hermann_mauguin': 'Pc21b', 'hermann_mauguin_u': 'Pc2_1b', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', '-x,y+1/2,-z'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'Pc2_1b', 'symops': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', '-x,y+1/2,-z'], 'universal_h_m': 'Pc21b'}, {'hall': ' P -2a -2ab', 'hermann_mauguin': 'Pb21a', 'hermann_mauguin_u': 'Pb2_1a', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y+1/2,z', '-x,y+1/2,-z'], 'number': 29, 'point_group': 'mm2', 'schoenflies': 'C2v^5', 'short_h_m': 'Pb2_1a', 'symops': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y+1/2,z', '-x,y+1/2,-z'], 'universal_h_m': 'Pb21a'}, {'hall': ' P 2 -2bc', 'hermann_mauguin': 'Pnc2', 'hermann_mauguin_u': 'Pnc2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'Pnc2', 'symops': ['x,y,z', '-x,-y,z', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Pnc2'}, {'hall': ' P 2 -2ac', 'hermann_mauguin': 'Pcn2', 'hermann_mauguin_u': 'Pcn2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'Pcn2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Pcn2'}, {'hall': ' P -2ac 2', 'hermann_mauguin': 'P2na', 'hermann_mauguin_u': 'P2na', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', 'x,-y,-z', 'x+1/2,-y,z+1/2'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'P2na', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', 'x,-y,-z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P2na'}, {'hall': ' P -2ab 2', 'hermann_mauguin': 'P2an', 'hermann_mauguin_u': 'P2an', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', 'x,-y,-z', 'x+1/2,-y+1/2,z'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'P2an', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', 'x,-y,-z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P2an'}, {'hall': ' P -2ab -2ab', 'hermann_mauguin': 'Pb2n', 'hermann_mauguin_u': 'Pb2n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x,y,-z'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'Pb2n', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x,y,-z'], 'universal_h_m': 'Pb2n'}, {'hall': ' P -2bc -2bc', 'hermann_mauguin': 'Pn2b', 'hermann_mauguin_u': 'Pn2b', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-x,y,-z'], 'number': 30, 'point_group': 'mm2', 'schoenflies': 'C2v^6', 'short_h_m': 'Pn2b', 'symops': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-x,y,-z'], 'universal_h_m': 'Pn2b'}, {'hall': ' P 2ac -2', 'hermann_mauguin': 'Pmn21', 'hermann_mauguin_u': 'Pmn2_1', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'Pmn2_1', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,y,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Pmn21'}, {'hall': ' P 2bc -2bc', 'hermann_mauguin': 'Pnm21', 'hermann_mauguin_u': 'Pnm2_1', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'Pnm2_1', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z'], 'universal_h_m': 'Pnm21'}, {'hall': ' P -2ab 2ab', 'hermann_mauguin': 'P21mn', 'hermann_mauguin_u': 'P2_1mn', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,-z', 'x,-y,z'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'P2_1mn', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,-z', 'x,-y,z'], 'universal_h_m': 'P21mn'}, {'hall': ' P -2 2ac', 'hermann_mauguin': 'P21nm', 'hermann_mauguin_u': 'P2_1nm', 'ncsym': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'P2_1nm', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P21nm'}, {'hall': ' P -2 -2bc', 'hermann_mauguin': 'Pn21m', 'hermann_mauguin_u': 'Pn2_1m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'Pn2_1m', 'symops': ['x,y,z', 'x,y,-z', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'Pn21m'}, {'hall': ' P -2ab -2', 'hermann_mauguin': 'Pm21n', 'hermann_mauguin_u': 'Pm2_1n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x,y,z', '-x+1/2,y+1/2,-z'], 'number': 31, 'point_group': 'mm2', 'schoenflies': 'C2v^7', 'short_h_m': 'Pm2_1n', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', '-x,y,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Pm21n'}, {'hall': ' P 2 -2ab', 'hermann_mauguin': 'Pba2', 'hermann_mauguin_u': 'Pba2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 32, 'point_group': 'mm2', 'schoenflies': 'C2v^8', 'short_h_m': 'Pba2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Pba2'}, {'hall': ' P -2bc 2', 'hermann_mauguin': 'P2cb', 'hermann_mauguin_u': 'P2cb', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', 'x,-y,-z', 'x,-y+1/2,z+1/2'], 'number': 32, 'point_group': 'mm2', 'schoenflies': 'C2v^8', 'short_h_m': 'P2cb', 'symops': ['x,y,z', 'x,y+1/2,-z+1/2', 'x,-y,-z', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'P2cb'}, {'hall': ' P -2ac -2ac', 'hermann_mauguin': 'Pc2a', 'hermann_mauguin_u': 'Pc2a', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x,y,-z'], 'number': 32, 'point_group': 'mm2', 'schoenflies': 'C2v^8', 'short_h_m': 'Pc2a', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x,y,-z'], 'universal_h_m': 'Pc2a'}, {'hall': ' P 2c -2n', 'hermann_mauguin': 'Pna21', 'hermann_mauguin_u': 'Pna2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'Pna2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Pna21'}, {'hall': ' P 2c -2ab', 'hermann_mauguin': 'Pbn21', 'hermann_mauguin_u': 'Pbn2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'Pbn2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Pbn21'}, {'hall': ' P -2bc 2a', 'hermann_mauguin': 'P21nb', 'hermann_mauguin_u': 'P2_1nb', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,-y,-z', 'x+1/2,-y+1/2,z+1/2'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'P2_1nb', 'symops': ['x,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,-y,-z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P21nb'}, {'hall': ' P -2n 2a', 'hermann_mauguin': 'P21cn', 'hermann_mauguin_u': 'P2_1cn', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y,-z', 'x,-y+1/2,z+1/2'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'P2_1cn', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y,-z', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'P21cn'}, {'hall': ' P -2n -2ac', 'hermann_mauguin': 'Pc21n', 'hermann_mauguin_u': 'Pc2_1n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', '-x,y+1/2,-z'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'Pc2_1n', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', '-x,y+1/2,-z'], 'universal_h_m': 'Pc21n'}, {'hall': ' P -2ac -2n', 'hermann_mauguin': 'Pn21a', 'hermann_mauguin_u': 'Pn2_1a', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z'], 'number': 33, 'point_group': 'mm2', 'schoenflies': 'C2v^9', 'short_h_m': 'Pn2_1a', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z'], 'universal_h_m': 'Pn21a'}, {'hall': ' P 2 -2n', 'hermann_mauguin': 'Pnn2', 'hermann_mauguin_u': 'Pnn2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 34, 'point_group': 'mm2', 'schoenflies': 'C2v^10', 'short_h_m': 'Pnn2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Pnn2'}, {'hall': ' P -2n 2', 'hermann_mauguin': 'P2nn', 'hermann_mauguin_u': 'P2nn', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', 'x,-y,-z', 'x+1/2,-y+1/2,z+1/2'], 'number': 34, 'point_group': 'mm2', 'schoenflies': 'C2v^10', 'short_h_m': 'P2nn', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', 'x,-y,-z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P2nn'}, {'hall': ' P -2n -2n', 'hermann_mauguin': 'Pn2n', 'hermann_mauguin_u': 'Pn2n', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y,-z'], 'number': 34, 'point_group': 'mm2', 'schoenflies': 'C2v^10', 'short_h_m': 'Pn2n', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y,-z'], 'universal_h_m': 'Pn2n'}, {'hall': ' C 2 -2', 'hermann_mauguin': 'Cmm2', 'hermann_mauguin_u': 'Cmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'Cmm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Cmm2'}, {'hall': ' A -2 2', 'hermann_mauguin': 'A2mm', 'hermann_mauguin_u': 'A2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'A2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'A2mm'}, {'hall': ' B -2 -2', 'hermann_mauguin': 'Bm2m', 'hermann_mauguin_u': 'Bm2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'Bm2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2'], 'universal_h_m': 'Bm2m'}, {'hall': ' C 2c -2', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Cmc21'}, {'hall': ' C 2c -2c', 'hermann_mauguin': 'Ccm21', 'hermann_mauguin_u': 'Ccm2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Ccm2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Ccm21'}, {'hall': ' A -2a 2a', 'hermann_mauguin': 'A21ma', 'hermann_mauguin_u': 'A2_1ma', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,-y,-z', 'x,-y,z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'A2_1ma', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,-y,-z', 'x,-y,z', 'x,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'A21ma'}, {'hall': ' A -2 2a', 'hermann_mauguin': 'A21am', 'hermann_mauguin_u': 'A2_1am', 'ncsym': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z', 'x+1/2,-y,z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'A2_1am', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,-y,-z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'A21am'}, {'hall': ' B -2 -2b', 'hermann_mauguin': 'Bb21m', 'hermann_mauguin_u': 'Bb2_1m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Bb2_1m', 'symops': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Bb21m'}, {'hall': ' B -2b -2', 'hermann_mauguin': 'Bm21b', 'hermann_mauguin_u': 'Bm2_1b', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Bm2_1b', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z', 'x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Bm21b'}, {'hall': ' C 2 -2c', 'hermann_mauguin': 'Ccc2', 'hermann_mauguin_u': 'Ccc2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'number': 37, 'point_group': 'mm2', 'schoenflies': 'C2v^13', 'short_h_m': 'Ccc2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Ccc2'}, {'hall': ' A -2a 2', 'hermann_mauguin': 'A2aa', 'hermann_mauguin_u': 'A2aa', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'number': 37, 'point_group': 'mm2', 'schoenflies': 'C2v^13', 'short_h_m': 'A2aa', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'A2aa'}, {'hall': ' B -2b -2b', 'hermann_mauguin': 'Bb2b', 'hermann_mauguin_u': 'Bb2b', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'number': 37, 'point_group': 'mm2', 'schoenflies': 'C2v^13', 'short_h_m': 'Bb2b', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z', 'x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x+1/2,y,-z+1/2'], 'universal_h_m': 'Bb2b'}, {'hall': ' A 2 -2', 'hermann_mauguin': 'Amm2', 'hermann_mauguin_u': 'Amm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Amm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Amm2'}, {'hall': ' B 2 -2', 'hermann_mauguin': 'Bmm2', 'hermann_mauguin_u': 'Bmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Bmm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Bmm2'}, {'hall': ' B -2 2', 'hermann_mauguin': 'B2mm', 'hermann_mauguin_u': 'B2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'B2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2', 'x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'B2mm'}, {'hall': ' C -2 2', 'hermann_mauguin': 'C2mm', 'hermann_mauguin_u': 'C2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'C2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'C2mm'}, {'hall': ' C -2 -2', 'hermann_mauguin': 'Cm2m', 'hermann_mauguin_u': 'Cm2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Cm2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Cm2m'}, {'hall': ' A -2 -2', 'hermann_mauguin': 'Am2m', 'hermann_mauguin_u': 'Am2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Am2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'Am2m'}, {'hall': ' A 2 -2b', 'hermann_mauguin': 'Aem2', 'hermann_mauguin_u': 'Aem2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Aem2', 'symops': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,y+1,z+1/2', 'x,-y+1,z+1/2'], 'universal_h_m': 'Aem2'}, {'hall': ' B 2 -2a', 'hermann_mauguin': 'Bme2', 'hermann_mauguin_u': 'Bme2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Bme2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1,y,z+1/2', 'x+1,-y,z+1/2'], 'universal_h_m': 'Bme2'}, {'hall': ' B -2a 2', 'hermann_mauguin': 'B2em', 'hermann_mauguin_u': 'B2em', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'B2em', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z', 'x+1/2,y,z+1/2', 'x+1,y,-z+1/2', 'x+1/2,-y,-z+1/2', 'x+1,-y,z+1/2'], 'universal_h_m': 'B2em'}, {'hall': ' C -2a 2', 'hermann_mauguin': 'C2me', 'hermann_mauguin_u': 'C2me', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'C2me', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z', 'x+1/2,y+1/2,z', 'x+1,y+1/2,-z', 'x+1/2,-y+1/2,-z', 'x+1,-y+1/2,z'], 'universal_h_m': 'C2me'}, {'hall': ' C -2a -2a', 'hermann_mauguin': 'Cm2e', 'hermann_mauguin_u': 'Cm2e', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Cm2e', 'symops': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z', 'x+1/2,y+1/2,z', 'x+1,y+1/2,-z', '-x+1,y+1/2,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Cm2e'}, {'hall': ' A -2b -2b', 'hermann_mauguin': 'Ae2m', 'hermann_mauguin_u': 'Ae2m', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Ae2m', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z', 'x,y+1/2,z+1/2', 'x,y+1,-z+1/2', '-x,y+1,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'Ae2m'}, {'hall': ' A 2 -2a', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Ama2'}, {'hall': ' B 2 -2b', 'hermann_mauguin': 'Bbm2', 'hermann_mauguin_u': 'Bbm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Bbm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Bbm2'}, {'hall': ' B -2b 2', 'hermann_mauguin': 'B2mb', 'hermann_mauguin_u': 'B2mb', 'ncsym': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'B2mb', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z', 'x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y,-z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'B2mb'}, {'hall': ' C -2c 2', 'hermann_mauguin': 'C2cm', 'hermann_mauguin_u': 'C2cm', 'ncsym': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'C2cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'C2cm'}, {'hall': ' C -2c -2c', 'hermann_mauguin': 'Cc2m', 'hermann_mauguin_u': 'Cc2m', 'ncsym': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Cc2m', 'symops': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Cc2m'}, {'hall': ' A -2a -2a', 'hermann_mauguin': 'Am2a', 'hermann_mauguin_u': 'Am2a', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Am2a', 'symops': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z', 'x,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'Am2a'}, {'hall': ' A 2 -2ab', 'hermann_mauguin': 'Aea2', 'hermann_mauguin_u': 'Aea2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Aea2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x+1/2,y+1,z+1/2', 'x+1/2,-y+1,z+1/2'], 'universal_h_m': 'Aea2'}, {'hall': ' B 2 -2ab', 'hermann_mauguin': 'Bbe2', 'hermann_mauguin_u': 'Bbe2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Bbe2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1,y+1/2,z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'Bbe2'}, {'hall': ' B -2ab 2', 'hermann_mauguin': 'B2eb', 'hermann_mauguin_u': 'B2eb', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', 'x,-y,-z', 'x+1/2,-y+1/2,z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'B2eb', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', 'x,-y,-z', 'x+1/2,-y+1/2,z', 'x+1/2,y,z+1/2', 'x+1,y+1/2,-z+1/2', 'x+1/2,-y,-z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'B2eb'}, {'hall': ' C -2ac 2', 'hermann_mauguin': 'C2eb', 'hermann_mauguin_u': 'C2eb', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', 'x,-y,-z', 'x+1/2,-y,z+1/2'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'C2eb', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', 'x,-y,-z', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'C2eb'}, {'hall': ' C -2ac -2ac', 'hermann_mauguin': 'Cc2e', 'hermann_mauguin_u': 'Cc2e', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x,y,-z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Cc2e', 'symops': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x,y,-z', 'x+1/2,y+1/2,z', 'x+1,y+1/2,-z+1/2', '-x+1,y+1/2,z+1/2', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Cc2e'}, {'hall': ' A -2ab -2ab', 'hermann_mauguin': 'Ae2a', 'hermann_mauguin_u': 'Ae2a', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x,y,-z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Ae2a', 'symops': ['x,y,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x,y,-z', 'x,y+1/2,z+1/2', 'x+1/2,y+1,-z+1/2', '-x+1/2,y+1,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'Ae2a'}, {'hall': ' F 2 -2', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Fmm2'}, {'hall': ' F -2 2', 'hermann_mauguin': 'F2mm', 'hermann_mauguin_u': 'F2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'F2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2', 'x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'F2mm'}, {'hall': ' F -2 -2', 'hermann_mauguin': 'Fm2m', 'hermann_mauguin_u': 'Fm2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fm2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'Fm2m'}, {'hall': ' F 2 -2d', 'hermann_mauguin': 'Fdd2', 'hermann_mauguin_u': 'Fdd2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/4,y+1/4,z+1/4', 'x+3/4,-y+3/4,z+1/4'], 'number': 43, 'point_group': 'mm2', 'schoenflies': 'C2v^19', 'short_h_m': 'Fdd2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/4,y+1/4,z+1/4', 'x+3/4,-y+3/4,z+1/4', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x+1/4,y+3/4,z+3/4', 'x+3/4,-y+5/4,z+3/4', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+3/4,y+1/4,z+3/4', 'x+5/4,-y+3/4,z+3/4', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+3/4,y+3/4,z+1/4', 'x+5/4,-y+5/4,z+1/4'], 'universal_h_m': 'Fdd2'}, {'hall': ' F -2d 2', 'hermann_mauguin': 'F2dd', 'hermann_mauguin_u': 'F2dd', 'ncsym': ['x,y,z', 'x+1/4,y+1/4,-z+1/4', 'x,-y,-z', 'x+1/4,-y+1/4,z+1/4'], 'number': 43, 'point_group': 'mm2', 'schoenflies': 'C2v^19', 'short_h_m': 'F2dd', 'symops': ['x,y,z', 'x+1/4,y+1/4,-z+1/4', 'x,-y,-z', 'x+1/4,-y+1/4,z+1/4', 'x,y+1/2,z+1/2', 'x+1/4,y+3/4,-z+3/4', 'x,-y+1/2,-z+1/2', 'x+1/4,-y+3/4,z+3/4', 'x+1/2,y,z+1/2', 'x+3/4,y+1/4,-z+3/4', 'x+1/2,-y,-z+1/2', 'x+3/4,-y+1/4,z+3/4', 'x+1/2,y+1/2,z', 'x+3/4,y+3/4,-z+1/4', 'x+1/2,-y+1/2,-z', 'x+3/4,-y+3/4,z+1/4'], 'universal_h_m': 'F2dd'}, {'hall': ' F -2d -2d', 'hermann_mauguin': 'Fd2d', 'hermann_mauguin_u': 'Fd2d', 'ncsym': ['x,y,z', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', '-x+1/2,y+1/2,-z'], 'number': 43, 'point_group': 'mm2', 'schoenflies': 'C2v^19', 'short_h_m': 'Fd2d', 'symops': ['x,y,z', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', '-x+1/2,y+1/2,-z', 'x,y+1/2,z+1/2', 'x+1/4,y+3/4,-z+3/4', '-x+1/4,y+3/4,z+3/4', '-x+1/2,y+1,-z+1/2', 'x+1/2,y,z+1/2', 'x+3/4,y+1/4,-z+3/4', '-x+3/4,y+1/4,z+3/4', '-x+1,y+1/2,-z+1/2', 'x+1/2,y+1/2,z', 'x+3/4,y+3/4,-z+1/4', '-x+3/4,y+3/4,z+1/4', '-x+1,y+1,-z'], 'universal_h_m': 'Fd2d'}, {'hall': ' I 2 -2', 'hermann_mauguin': 'Imm2', 'hermann_mauguin_u': 'Imm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Imm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Imm2'}, {'hall': ' I -2 2', 'hermann_mauguin': 'I2mm', 'hermann_mauguin_u': 'I2mm', 'ncsym': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'I2mm', 'symops': ['x,y,z', 'x,y,-z', 'x,-y,-z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'I2mm'}, {'hall': ' I -2 -2', 'hermann_mauguin': 'Im2m', 'hermann_mauguin_u': 'Im2m', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Im2m', 'symops': ['x,y,z', 'x,y,-z', '-x,y,z', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Im2m'}, {'hall': ' I 2 -2c', 'hermann_mauguin': 'Iba2', 'hermann_mauguin_u': 'Iba2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'number': 45, 'point_group': 'mm2', 'schoenflies': 'C2v^21', 'short_h_m': 'Iba2', 'symops': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1', 'x+1/2,-y+1/2,z+1'], 'universal_h_m': 'Iba2'}, {'hall': ' I -2a 2', 'hermann_mauguin': 'I2cb', 'hermann_mauguin_u': 'I2cb', 'ncsym': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z'], 'number': 45, 'point_group': 'mm2', 'schoenflies': 'C2v^21', 'short_h_m': 'I2cb', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x,-y,-z', 'x+1/2,-y,z', 'x+1/2,y+1/2,z+1/2', 'x+1,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'I2cb'}, {'hall': ' I -2b -2b', 'hermann_mauguin': 'Ic2a', 'hermann_mauguin_u': 'Ic2a', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'number': 45, 'point_group': 'mm2', 'schoenflies': 'C2v^21', 'short_h_m': 'Ic2a', 'symops': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1,-z+1/2', '-x+1/2,y+1,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Ic2a'}, {'hall': ' I 2 -2a', 'hermann_mauguin': 'Ima2', 'hermann_mauguin_u': 'Ima2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ima2', 'symops': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1,y+1/2,z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'Ima2'}, {'hall': ' I 2 -2b', 'hermann_mauguin': 'Ibm2', 'hermann_mauguin_u': 'Ibm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ibm2', 'symops': ['x,y,z', '-x,-y,z', '-x,y+1/2,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1,z+1/2', 'x+1/2,-y+1,z+1/2'], 'universal_h_m': 'Ibm2'}, {'hall': ' I -2b 2', 'hermann_mauguin': 'I2mb', 'hermann_mauguin_u': 'I2mb', 'ncsym': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'I2mb', 'symops': ['x,y,z', 'x,y+1/2,-z', 'x,-y,-z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1,z+1/2'], 'universal_h_m': 'I2mb'}, {'hall': ' I -2c 2', 'hermann_mauguin': 'I2cm', 'hermann_mauguin_u': 'I2cm', 'ncsym': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'I2cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x,-y,-z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1', 'x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1'], 'universal_h_m': 'I2cm'}, {'hall': ' I -2c -2c', 'hermann_mauguin': 'Ic2m', 'hermann_mauguin_u': 'Ic2m', 'ncsym': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ic2m', 'symops': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1', '-x+1/2,y+1/2,z+1', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Ic2m'}, {'hall': ' I -2a -2a', 'hermann_mauguin': 'Im2a', 'hermann_mauguin_u': 'Im2a', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Im2a', 'symops': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y,z', '-x,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1,y+1/2,-z+1/2', '-x+1,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Im2a'}, {'hall': '-P 2 2', 'hermann_mauguin': 'Pmmm', 'hermann_mauguin_u': 'Pmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 47, 'point_group': 'mmm', 'schoenflies': 'D2h^1', 'short_h_m': 'Pmmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'universal_h_m': 'Pmmm'}, {'hall': ' P 2 2 -1n', 'hermann_mauguin': 'Pnnn', 'hermann_mauguin_u': 'Pnnn', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 48, 'point_group': 'mmm', 'schoenflies': 'D2h^2', 'short_h_m': 'Pnnn', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Pnnn:1'}, {'hall': '-P 2ab 2bc', 'hermann_mauguin': 'Pnnn', 'hermann_mauguin_u': 'Pnnn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y,z-1/2'], 'number': 48, 'point_group': 'mmm', 'schoenflies': 'D2h^2', 'short_h_m': 'Pnnn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pnnn:2'}, {'hall': '-P 2 2c', 'hermann_mauguin': 'Pccm', 'hermann_mauguin_u': 'Pccm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2'], 'number': 49, 'point_group': 'mmm', 'schoenflies': 'D2h^3', 'short_h_m': 'Pccm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2'], 'universal_h_m': 'Pccm'}, {'hall': '-P 2a 2', 'hermann_mauguin': 'Pmaa', 'hermann_mauguin_u': 'Pmaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'number': 49, 'point_group': 'mmm', 'schoenflies': 'D2h^3', 'short_h_m': 'Pmaa', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'universal_h_m': 'Pmaa'}, {'hall': '-P 2b 2b', 'hermann_mauguin': 'Pbmb', 'hermann_mauguin_u': 'Pbmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z'], 'number': 49, 'point_group': 'mmm', 'schoenflies': 'D2h^3', 'short_h_m': 'Pbmb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z'], 'universal_h_m': 'Pbmb'}, {'hall': ' P 2 2 -1ab', 'hermann_mauguin': 'Pban', 'hermann_mauguin_u': 'Pban', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pban', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Pban:1'}, {'hall': '-P 2ab 2b', 'hermann_mauguin': 'Pban', 'hermann_mauguin_u': 'Pban', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pban', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z'], 'universal_h_m': 'Pban:2'}, {'hall': ' P 2 2 -1bc', 'hermann_mauguin': 'Pncb', 'hermann_mauguin_u': 'Pncb', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pncb', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Pncb:1'}, {'hall': '-P 2b 2bc', 'hermann_mauguin': 'Pncb', 'hermann_mauguin_u': 'Pncb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z-1/2', 'x,-y,z-1/2'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pncb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z-1/2', 'x,-y,z-1/2'], 'universal_h_m': 'Pncb:2'}, {'hall': ' P 2 2 -1ac', 'hermann_mauguin': 'Pcna', 'hermann_mauguin_u': 'Pcna', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pcna', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Pcna:1'}, {'hall': '-P 2a 2c', 'hermann_mauguin': 'Pcna', 'hermann_mauguin_u': 'Pcna', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z-1/2', 'x-1/2,-y,z-1/2'], 'number': 50, 'point_group': 'mmm', 'schoenflies': 'D2h^4', 'short_h_m': 'Pcna', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z-1/2', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pcna:2'}, {'hall': '-P 2a 2a', 'hermann_mauguin': 'Pmma', 'hermann_mauguin_u': 'Pmma', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmma', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z'], 'universal_h_m': 'Pmma'}, {'hall': '-P 2b 2', 'hermann_mauguin': 'Pmmb', 'hermann_mauguin_u': 'Pmmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmmb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z'], 'universal_h_m': 'Pmmb'}, {'hall': '-P 2 2b', 'hermann_mauguin': 'Pbmm', 'hermann_mauguin_u': 'Pbmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pbmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z'], 'universal_h_m': 'Pbmm'}, {'hall': '-P 2c 2c', 'hermann_mauguin': 'Pcmm', 'hermann_mauguin_u': 'Pcmm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pcmm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z'], 'universal_h_m': 'Pcmm'}, {'hall': '-P 2c 2', 'hermann_mauguin': 'Pmcm', 'hermann_mauguin_u': 'Pmcm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmcm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2'], 'universal_h_m': 'Pmcm'}, {'hall': '-P 2 2a', 'hermann_mauguin': 'Pmam', 'hermann_mauguin_u': 'Pmam', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmam', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z'], 'universal_h_m': 'Pmam'}, {'hall': '-P 2a 2bc', 'hermann_mauguin': 'Pnna', 'hermann_mauguin_u': 'Pnna', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pnna', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pnna'}, {'hall': '-P 2b 2n', 'hermann_mauguin': 'Pnnb', 'hermann_mauguin_u': 'Pnnb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y,z-1/2'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pnnb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pnnb'}, {'hall': '-P 2n 2b', 'hermann_mauguin': 'Pbnn', 'hermann_mauguin_u': 'Pbnn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y-1/2,z', 'x-1/2,-y,z-1/2'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pbnn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y-1/2,z', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pbnn'}, {'hall': '-P 2ab 2c', 'hermann_mauguin': 'Pcnn', 'hermann_mauguin_u': 'Pcnn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pcnn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pcnn'}, {'hall': '-P 2ab 2n', 'hermann_mauguin': 'Pncn', 'hermann_mauguin_u': 'Pncn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z-1/2', 'x,-y,z-1/2'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pncn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z-1/2', 'x,-y,z-1/2'], 'universal_h_m': 'Pncn'}, {'hall': '-P 2n 2bc', 'hermann_mauguin': 'Pnan', 'hermann_mauguin_u': 'Pnan', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y-1/2,z-1/2', 'x-1/2,-y,z'], 'number': 52, 'point_group': 'mmm', 'schoenflies': 'D2h^6', 'short_h_m': 'Pnan', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y-1/2,z-1/2', 'x-1/2,-y,z'], 'universal_h_m': 'Pnan'}, {'hall': '-P 2ac 2', 'hermann_mauguin': 'Pmna', 'hermann_mauguin_u': 'Pmna', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z', 'x-1/2,-y,z-1/2'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pmna', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pmna'}, {'hall': '-P 2bc 2bc', 'hermann_mauguin': 'Pnmb', 'hermann_mauguin_u': 'Pnmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y-1/2,z-1/2', 'x,-y,z'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pnmb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y-1/2,z-1/2', 'x,-y,z'], 'universal_h_m': 'Pnmb'}, {'hall': '-P 2ab 2ab', 'hermann_mauguin': 'Pbmn', 'hermann_mauguin_u': 'Pbmn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z', 'x,-y,z'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pbmn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z', 'x,-y,z'], 'universal_h_m': 'Pbmn'}, {'hall': '-P 2 2ac', 'hermann_mauguin': 'Pcnm', 'hermann_mauguin_u': 'Pcnm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z-1/2', 'x-1/2,-y,z-1/2'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pcnm', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z-1/2', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pcnm'}, {'hall': '-P 2 2bc', 'hermann_mauguin': 'Pncm', 'hermann_mauguin_u': 'Pncm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z-1/2', 'x,-y-1/2,z-1/2'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pncm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z-1/2', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pncm'}, {'hall': '-P 2ab 2', 'hermann_mauguin': 'Pman', 'hermann_mauguin_u': 'Pman', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z', 'x-1/2,-y-1/2,z'], 'number': 53, 'point_group': 'mmm', 'schoenflies': 'D2h^7', 'short_h_m': 'Pman', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pman'}, {'hall': '-P 2a 2ac', 'hermann_mauguin': 'Pcca', 'hermann_mauguin_u': 'Pcca', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z-1/2', 'x,-y,z-1/2'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pcca', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z-1/2', 'x,-y,z-1/2'], 'universal_h_m': 'Pcca'}, {'hall': '-P 2b 2c', 'hermann_mauguin': 'Pccb', 'hermann_mauguin_u': 'Pccb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pccb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pccb'}, {'hall': '-P 2a 2b', 'hermann_mauguin': 'Pbaa', 'hermann_mauguin_u': 'Pbaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pbaa', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pbaa'}, {'hall': '-P 2ac 2c', 'hermann_mauguin': 'Pcaa', 'hermann_mauguin_u': 'Pcaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z-1/2', 'x-1/2,-y,z'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pcaa', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z-1/2', 'x-1/2,-y,z'], 'universal_h_m': 'Pcaa'}, {'hall': '-P 2bc 2b', 'hermann_mauguin': 'Pbcb', 'hermann_mauguin_u': 'Pbcb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y-1/2,z', 'x,-y,z-1/2'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pbcb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y-1/2,z', 'x,-y,z-1/2'], 'universal_h_m': 'Pbcb'}, {'hall': '-P 2b 2ab', 'hermann_mauguin': 'Pbab', 'hermann_mauguin_u': 'Pbab', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y,z'], 'number': 54, 'point_group': 'mmm', 'schoenflies': 'D2h^8', 'short_h_m': 'Pbab', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y,z'], 'universal_h_m': 'Pbab'}, {'hall': '-P 2 2ab', 'hermann_mauguin': 'Pbam', 'hermann_mauguin_u': 'Pbam', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 55, 'point_group': 'mmm', 'schoenflies': 'D2h^9', 'short_h_m': 'Pbam', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pbam'}, {'hall': '-P 2bc 2', 'hermann_mauguin': 'Pmcb', 'hermann_mauguin_u': 'Pmcb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y,z', 'x,-y-1/2,z-1/2'], 'number': 55, 'point_group': 'mmm', 'schoenflies': 'D2h^9', 'short_h_m': 'Pmcb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y,z', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pmcb'}, {'hall': '-P 2ac 2ac', 'hermann_mauguin': 'Pcma', 'hermann_mauguin_u': 'Pcma', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y,z'], 'number': 55, 'point_group': 'mmm', 'schoenflies': 'D2h^9', 'short_h_m': 'Pcma', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y,z'], 'universal_h_m': 'Pcma'}, {'hall': '-P 2ab 2ac', 'hermann_mauguin': 'Pccn', 'hermann_mauguin_u': 'Pccn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y,z-1/2', 'x,-y-1/2,z-1/2'], 'number': 56, 'point_group': 'mmm', 'schoenflies': 'D2h^10', 'short_h_m': 'Pccn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y,z-1/2', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pccn'}, {'hall': '-P 2ac 2bc', 'hermann_mauguin': 'Pnaa', 'hermann_mauguin_u': 'Pnaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y-1/2,z-1/2', 'x-1/2,-y-1/2,z'], 'number': 56, 'point_group': 'mmm', 'schoenflies': 'D2h^10', 'short_h_m': 'Pnaa', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y-1/2,z-1/2', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pnaa'}, {'hall': '-P 2bc 2ab', 'hermann_mauguin': 'Pbnb', 'hermann_mauguin_u': 'Pbnb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y-1/2,z', 'x-1/2,-y,z-1/2'], 'number': 56, 'point_group': 'mmm', 'schoenflies': 'D2h^10', 'short_h_m': 'Pbnb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y-1/2,z', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pbnb'}, {'hall': '-P 2c 2b', 'hermann_mauguin': 'Pbcm', 'hermann_mauguin_u': 'Pbcm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y+1/2,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y-1/2,z', 'x,-y-1/2,z-1/2'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pbcm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y+1/2,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y-1/2,z', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pbcm'}, {'hall': '-P 2c 2ac', 'hermann_mauguin': 'Pcam', 'hermann_mauguin_u': 'Pcam', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y,z-1/2', 'x-1/2,-y,z'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pcam', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y,z-1/2', 'x-1/2,-y,z'], 'universal_h_m': 'Pcam'}, {'hall': '-P 2ac 2a', 'hermann_mauguin': 'Pmca', 'hermann_mauguin_u': 'Pmca', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z', 'x,-y,z-1/2'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pmca', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z', 'x,-y,z-1/2'], 'universal_h_m': 'Pmca'}, {'hall': '-P 2b 2a', 'hermann_mauguin': 'Pmab', 'hermann_mauguin_u': 'Pmab', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y,z', 'x-1/2,-y-1/2,z'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pmab', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y,z', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pmab'}, {'hall': '-P 2a 2ab', 'hermann_mauguin': 'Pbma', 'hermann_mauguin_u': 'Pbma', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y-1/2,z', 'x,-y-1/2,z'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pbma', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y-1/2,z', 'x,-y-1/2,z'], 'universal_h_m': 'Pbma'}, {'hall': '-P 2bc 2c', 'hermann_mauguin': 'Pcmb', 'hermann_mauguin_u': 'Pcmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y,z-1/2', 'x,-y-1/2,z'], 'number': 57, 'point_group': 'mmm', 'schoenflies': 'D2h^11', 'short_h_m': 'Pcmb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x,y,z-1/2', 'x,-y-1/2,z'], 'universal_h_m': 'Pcmb'}, {'hall': '-P 2 2n', 'hermann_mauguin': 'Pnnm', 'hermann_mauguin_u': 'Pnnm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'number': 58, 'point_group': 'mmm', 'schoenflies': 'D2h^12', 'short_h_m': 'Pnnm', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pnnm'}, {'hall': '-P 2n 2', 'hermann_mauguin': 'Pmnn', 'hermann_mauguin_u': 'Pmnn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y,z', 'x-1/2,-y-1/2,z-1/2'], 'number': 58, 'point_group': 'mmm', 'schoenflies': 'D2h^12', 'short_h_m': 'Pmnn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y,z', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pmnn'}, {'hall': '-P 2n 2n', 'hermann_mauguin': 'Pnmn', 'hermann_mauguin_u': 'Pnmn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x,-y,z'], 'number': 58, 'point_group': 'mmm', 'schoenflies': 'D2h^12', 'short_h_m': 'Pnmn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x,-y,z'], 'universal_h_m': 'Pnmn'}, {'hall': ' P 2 2ab -1ab', 'hermann_mauguin': 'Pmmn', 'hermann_mauguin_u': 'Pmmn', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y,z', 'x,-y,z'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pmmn', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y,z', 'x,-y,z'], 'universal_h_m': 'Pmmn:1'}, {'hall': '-P 2ab 2a', 'hermann_mauguin': 'Pmmn', 'hermann_mauguin_u': 'Pmmn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y,z', 'x,-y-1/2,z'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pmmn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y,z', 'x,-y-1/2,z'], 'universal_h_m': 'Pmmn:2'}, {'hall': ' P 2bc 2 -1bc', 'hermann_mauguin': 'Pnmm', 'hermann_mauguin_u': 'Pnmm', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pnmm', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y+1/2,z+1/2', 'x,-y,z'], 'universal_h_m': 'Pnmm:1'}, {'hall': '-P 2c 2bc', 'hermann_mauguin': 'Pnmm', 'hermann_mauguin_u': 'Pnmm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y-1/2,z-1/2', 'x,-y-1/2,z'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pnmm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y-1/2,z-1/2', 'x,-y-1/2,z'], 'universal_h_m': 'Pnmm:2'}, {'hall': ' P 2ac 2ac -1ac', 'hermann_mauguin': 'Pmnm', 'hermann_mauguin_u': 'Pmnm', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pmnm', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', '-x,y,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Pmnm:1'}, {'hall': '-P 2c 2a', 'hermann_mauguin': 'Pmnm', 'hermann_mauguin_u': 'Pmnm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y,z', 'x-1/2,-y,z-1/2'], 'number': 59, 'point_group': 'mmm', 'schoenflies': 'D2h^13', 'short_h_m': 'Pmnm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y,z', 'x-1/2,-y,z-1/2'], 'universal_h_m': 'Pmnm:2'}, {'hall': '-P 2n 2ab', 'hermann_mauguin': 'Pbcn', 'hermann_mauguin_u': 'Pbcn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y,z-1/2'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pbcn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y,z-1/2'], 'universal_h_m': 'Pbcn'}, {'hall': '-P 2n 2c', 'hermann_mauguin': 'Pcan', 'hermann_mauguin_u': 'Pcan', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y,z-1/2', 'x-1/2,-y-1/2,z'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pcan', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x,y,z-1/2', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pcan'}, {'hall': '-P 2a 2n', 'hermann_mauguin': 'Pnca', 'hermann_mauguin_u': 'Pnca', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y-1/2,z-1/2', 'x,-y-1/2,z-1/2'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pnca', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y-1/2,z-1/2', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pnca'}, {'hall': '-P 2bc 2n', 'hermann_mauguin': 'Pnab', 'hermann_mauguin_u': 'Pnab', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y,z'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pnab', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y,z'], 'universal_h_m': 'Pnab'}, {'hall': '-P 2ac 2b', 'hermann_mauguin': 'Pbna', 'hermann_mauguin_u': 'Pbna', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y-1/2,z', 'x-1/2,-y-1/2,z-1/2'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pbna', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y-1/2,z', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pbna'}, {'hall': '-P 2b 2ac', 'hermann_mauguin': 'Pcnb', 'hermann_mauguin_u': 'Pcnb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'number': 60, 'point_group': 'mmm', 'schoenflies': 'D2h^14', 'short_h_m': 'Pcnb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y,z-1/2', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pcnb'}, {'hall': '-P 2ac 2ab', 'hermann_mauguin': 'Pbca', 'hermann_mauguin_u': 'Pbca', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y-1/2,z-1/2'], 'number': 61, 'point_group': 'mmm', 'schoenflies': 'D2h^15', 'short_h_m': 'Pbca', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pbca'}, {'hall': '-P 2bc 2ac', 'hermann_mauguin': 'Pcab', 'hermann_mauguin_u': 'Pcab', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y,z-1/2', 'x-1/2,-y-1/2,z'], 'number': 61, 'point_group': 'mmm', 'schoenflies': 'D2h^15', 'short_h_m': 'Pcab', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y,z-1/2', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pcab'}, {'hall': '-P 2ac 2n', 'hermann_mauguin': 'Pnma', 'hermann_mauguin_u': 'Pnma', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x,-y-1/2,z'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pnma', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x,-y-1/2,z'], 'universal_h_m': 'Pnma'}, {'hall': '-P 2bc 2a', 'hermann_mauguin': 'Pmnb', 'hermann_mauguin_u': 'Pmnb', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y,z', 'x-1/2,-y-1/2,z-1/2'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pmnb', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z-1/2', '-x-1/2,y,z', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pmnb'}, {'hall': '-P 2c 2ab', 'hermann_mauguin': 'Pbnm', 'hermann_mauguin_u': 'Pbnm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z-1/2'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pbnm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z-1/2'], 'universal_h_m': 'Pbnm'}, {'hall': '-P 2n 2ac', 'hermann_mauguin': 'Pcmn', 'hermann_mauguin_u': 'Pcmn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y-1/2,z'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pcmn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y-1/2,z'], 'universal_h_m': 'Pcmn'}, {'hall': '-P 2n 2a', 'hermann_mauguin': 'Pmcn', 'hermann_mauguin_u': 'Pmcn', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y,z', 'x,-y-1/2,z-1/2'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pmcn', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x-1/2,y-1/2,-z-1/2', '-x-1/2,y,z', 'x,-y-1/2,z-1/2'], 'universal_h_m': 'Pmcn'}, {'hall': '-P 2c 2n', 'hermann_mauguin': 'Pnam', 'hermann_mauguin_u': 'Pnam', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y-1/2,z'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pnam', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x-1/2,y-1/2,z-1/2', 'x-1/2,-y-1/2,z'], 'universal_h_m': 'Pnam'}, {'hall': '-C 2c 2', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z-1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z-1/2'], 'universal_h_m': 'Cmcm'}, {'hall': '-C 2c 2c', 'hermann_mauguin': 'Ccmm', 'hermann_mauguin_u': 'Ccmm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Ccmm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z-1/2', '-x+1/2,y+1/2,z-1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Ccmm'}, {'hall': '-A 2a 2a', 'hermann_mauguin': 'Amma', 'hermann_mauguin_u': 'Amma', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Amma', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y+1/2,-z+1/2', '-x-1/2,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Amma'}, {'hall': '-A 2 2a', 'hermann_mauguin': 'Amam', 'hermann_mauguin_u': 'Amam', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Amam', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x-1/2,y+1/2,z+1/2', 'x-1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Amam'}, {'hall': '-B 2 2b', 'hermann_mauguin': 'Bbmm', 'hermann_mauguin_u': 'Bbmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Bbmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y-1/2,z+1/2', 'x+1/2,-y-1/2,z+1/2'], 'universal_h_m': 'Bbmm'}, {'hall': '-B 2b 2', 'hermann_mauguin': 'Bmmb', 'hermann_mauguin_u': 'Bmmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Bmmb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y-1/2,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y-1/2,z+1/2'], 'universal_h_m': 'Bmmb'}, {'hall': '-C 2ac 2', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z', 'x-1/2,-y,z-1/2'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x,y,z', 'x-1/2,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z-1/2', '-x+1/2,y+1/2,z', 'x,-y+1/2,z-1/2'], 'universal_h_m': 'Cmce'}, {'hall': '-C 2ac 2ac', 'hermann_mauguin': 'Ccme', 'hermann_mauguin_u': 'Ccme', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Ccme', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y,z-1/2', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z-1/2', '-x,y+1/2,z-1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Ccme'}, {'hall': '-A 2ab 2ab', 'hermann_mauguin': 'Aema', 'hermann_mauguin_u': 'Aema', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z', 'x,-y,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Aema', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x-1/2,y-1/2,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y,-z+1/2', '-x-1/2,y,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Aema'}, {'hall': '-A 2 2ab', 'hermann_mauguin': 'Aeam', 'hermann_mauguin_u': 'Aeam', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Aeam', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x+1/2,y+1,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x-1/2,y,z+1/2', 'x-1/2,-y,z+1/2'], 'universal_h_m': 'Aeam'}, {'hall': '-B 2 2ab', 'hermann_mauguin': 'Bbem', 'hermann_mauguin_u': 'Bbem', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Bbem', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x,y-1/2,z+1/2', 'x,-y-1/2,z+1/2'], 'universal_h_m': 'Bbem'}, {'hall': '-B 2ab 2', 'hermann_mauguin': 'Bmeb', 'hermann_mauguin_u': 'Bmeb', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z', 'x-1/2,-y-1/2,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Bmeb', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y,z', 'x-1/2,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,y-1/2,-z+1/2', '-x+1/2,y,z+1/2', 'x,-y-1/2,z+1/2'], 'universal_h_m': 'Bmeb'}, {'hall': '-C 2 2', 'hermann_mauguin': 'Cmmm', 'hermann_mauguin_u': 'Cmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Cmmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Cmmm'}, {'hall': '-A 2 2', 'hermann_mauguin': 'Ammm', 'hermann_mauguin_u': 'Ammm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Ammm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Ammm'}, {'hall': '-B 2 2', 'hermann_mauguin': 'Bmmm', 'hermann_mauguin_u': 'Bmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Bmmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Bmmm'}, {'hall': '-C 2 2c', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z-1/2', 'x+1/2,-y+1/2,z-1/2'], 'universal_h_m': 'Cccm'}, {'hall': '-A 2a 2', 'hermann_mauguin': 'Amaa', 'hermann_mauguin_u': 'Amaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Amaa', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x-1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Amaa'}, {'hall': '-B 2b 2b', 'hermann_mauguin': 'Bbmb', 'hermann_mauguin_u': 'Bbmb', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Bbmb', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y-1/2,-z+1/2', '-x+1/2,y-1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Bbmb'}, {'hall': '-C 2a 2', 'hermann_mauguin': 'Cmma', 'hermann_mauguin_u': 'Cmma', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Cmma', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z', 'x,-y+1/2,z'], 'universal_h_m': 'Cmma'}, {'hall': '-C 2a 2a', 'hermann_mauguin': 'Cmmb', 'hermann_mauguin_u': 'Cmmb', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Cmmb', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z', 'x+1,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Cmmb'}, {'hall': '-A 2b 2b', 'hermann_mauguin': 'Abmm', 'hermann_mauguin_u': 'Abmm', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Abmm', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1,z+1/2', 'x,-y+1,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x,y,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Abmm'}, {'hall': '-A 2 2b', 'hermann_mauguin': 'Acmm', 'hermann_mauguin_u': 'Acmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Acmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1,-z+1/2', '-x,y+1,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Acmm'}, {'hall': '-B 2 2a', 'hermann_mauguin': 'Bmcm', 'hermann_mauguin_u': 'Bmcm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Bmcm', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1,-y,-z+1/2', '-x+1,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x,y,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Bmcm'}, {'hall': '-B 2a 2', 'hermann_mauguin': 'Bmam', 'hermann_mauguin_u': 'Bmam', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'number': 67, 'point_group': 'mmm', 'schoenflies': 'D2h^21', 'short_h_m': 'Bmam', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z', 'x+1/2,y,z+1/2', '-x+1,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Bmam'}, {'hall': ' C 2 2 -1ac', 'hermann_mauguin': 'Ccce', 'hermann_mauguin_u': 'Ccce', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Ccce', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1,-y+1/2,-z+1/2', 'x+1,y+1/2,-z+1/2', '-x+1,y+1/2,z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'Ccce:1'}, {'hall': '-C 2a 2ac', 'hermann_mauguin': 'Ccca', 'hermann_mauguin_u': 'Ccca', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z-1/2', 'x,-y,z-1/2'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Ccca', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z-1/2', 'x,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z', 'x+1,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z', '-x,y+1/2,z-1/2', 'x+1/2,-y+1/2,z-1/2'], 'universal_h_m': 'Ccca:2'}, {'hall': '-C 2a 2c', 'hermann_mauguin': 'Cccb', 'hermann_mauguin_u': 'Cccb', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z-1/2', 'x-1/2,-y,z-1/2'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Cccb', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z-1/2', 'x-1/2,-y,z-1/2', 'x+1/2,y+1/2,z', '-x+1,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z-1/2', 'x,-y+1/2,z-1/2'], 'universal_h_m': 'Cccb:2'}, {'hall': ' A 2 2 -1ab', 'hermann_mauguin': 'Aeaa', 'hermann_mauguin_u': 'Aeaa', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Aeaa', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x+1/2,-y+1,-z+1/2', 'x+1/2,y+1,-z+1/2', '-x+1/2,y+1,z+1/2', 'x+1/2,-y+1,z+1/2'], 'universal_h_m': 'Aeaa:1'}, {'hall': '-A 2a 2b', 'hermann_mauguin': 'Abaa', 'hermann_mauguin_u': 'Abaa', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Abaa', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1,-z+1/2', '-x+1/2,y+1,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y+1/2,-z+1/2', '-x,y,z+1/2', 'x-1/2,-y,z+1/2'], 'universal_h_m': 'Abaa:2'}, {'hall': '-A 2ab 2b', 'hermann_mauguin': 'Acaa', 'hermann_mauguin_u': 'Acaa', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Acaa', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x,-y+1,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x-1/2,y,-z+1/2', '-x,y,z+1/2', 'x-1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Acaa:2'}, {'hall': ' B 2 2 -1ab', 'hermann_mauguin': 'Bbeb', 'hermann_mauguin_u': 'Bbeb', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Bbeb', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1,-y+1/2,-z+1/2', 'x+1,y+1/2,-z+1/2', '-x+1,y+1/2,z+1/2', 'x+1,-y+1/2,z+1/2'], 'universal_h_m': 'Bbeb:1'}, {'hall': '-B 2ab 2b', 'hermann_mauguin': 'Bbcb', 'hermann_mauguin_u': 'Bbcb', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Bbcb', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z', 'x-1/2,-y,z', 'x+1/2,y,z+1/2', '-x+1,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,y-1/2,-z+1/2', '-x+1/2,y-1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Bbcb:2'}, {'hall': '-B 2b 2ab', 'hermann_mauguin': 'Bbab', 'hermann_mauguin_u': 'Bbab', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y,z'], 'number': 68, 'point_group': 'mmm', 'schoenflies': 'D2h^22', 'short_h_m': 'Bbab', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x-1/2,y-1/2,z', 'x-1/2,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y-1/2,-z+1/2', '-x,y-1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Bbab:2'}, {'hall': '-F 2 2', 'hermann_mauguin': 'Fmmm', 'hermann_mauguin_u': 'Fmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 69, 'point_group': 'mmm', 'schoenflies': 'D2h^23', 'short_h_m': 'Fmmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Fmmm'}, {'hall': ' F 2 2 -1d', 'hermann_mauguin': 'Fddd', 'hermann_mauguin_u': 'Fddd', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/4,-y+1/4,-z+1/4', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', 'x+1/4,-y+1/4,z+1/4'], 'number': 70, 'point_group': 'mmm', 'schoenflies': 'D2h^24', 'short_h_m': 'Fddd', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/4,-y+1/4,-z+1/4', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', 'x+1/4,-y+1/4,z+1/4', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x+1/4,-y+3/4,-z+3/4', 'x+1/4,y+3/4,-z+3/4', '-x+1/4,y+3/4,z+3/4', 'x+1/4,-y+3/4,z+3/4', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+3/4,-y+1/4,-z+3/4', 'x+3/4,y+1/4,-z+3/4', '-x+3/4,y+1/4,z+3/4', 'x+3/4,-y+1/4,z+3/4', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+3/4,-y+3/4,-z+1/4', 'x+3/4,y+3/4,-z+1/4', '-x+3/4,y+3/4,z+1/4', 'x+3/4,-y+3/4,z+1/4'], 'universal_h_m': 'Fddd:1'}, {'hall': '-F 2uv 2vw', 'hermann_mauguin': 'Fddd', 'hermann_mauguin_u': 'Fddd', 'ncsym': ['x,y,z', '-x+1/4,-y+1/4,z', 'x,-y+1/4,-z+1/4', '-x+1/4,y,-z+1/4', '-x,-y,-z', 'x-1/4,y-1/4,-z', '-x,y-1/4,z-1/4', 'x-1/4,-y,z-1/4'], 'number': 70, 'point_group': 'mmm', 'schoenflies': 'D2h^24', 'short_h_m': 'Fddd', 'symops': ['x,y,z', '-x+1/4,-y+1/4,z', 'x,-y+1/4,-z+1/4', '-x+1/4,y,-z+1/4', '-x,-y,-z', 'x-1/4,y-1/4,-z', '-x,y-1/4,z-1/4', 'x-1/4,-y,z-1/4', 'x,y+1/2,z+1/2', '-x+1/4,-y+3/4,z+1/2', 'x,-y+3/4,-z+3/4', '-x+1/4,y+1/2,-z+3/4', '-x,-y+1/2,-z+1/2', 'x-1/4,y+1/4,-z+1/2', '-x,y+1/4,z+1/4', 'x-1/4,-y+1/2,z+1/4', 'x+1/2,y,z+1/2', '-x+3/4,-y+1/4,z+1/2', 'x+1/2,-y+1/4,-z+3/4', '-x+3/4,y,-z+3/4', '-x+1/2,-y,-z+1/2', 'x+1/4,y-1/4,-z+1/2', '-x+1/2,y-1/4,z+1/4', 'x+1/4,-y,z+1/4', 'x+1/2,y+1/2,z', '-x+3/4,-y+3/4,z', 'x+1/2,-y+3/4,-z+1/4', '-x+3/4,y+1/2,-z+1/4', '-x+1/2,-y+1/2,-z', 'x+1/4,y+1/4,-z', '-x+1/2,y+1/4,z-1/4', 'x+1/4,-y+1/2,z-1/4'], 'universal_h_m': 'Fddd:2'}, {'hall': '-I 2 2', 'hermann_mauguin': 'Immm', 'hermann_mauguin_u': 'Immm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z'], 'number': 71, 'point_group': 'mmm', 'schoenflies': 'D2h^25', 'short_h_m': 'Immm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Immm'}, {'hall': '-I 2 2c', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z-1/2', 'x,-y,z-1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1/2,-z+1', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Ibam'}, {'hall': '-I 2a 2', 'hermann_mauguin': 'Imcb', 'hermann_mauguin_u': 'Imcb', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Imcb', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y,z', 'x-1/2,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Imcb'}, {'hall': '-I 2b 2b', 'hermann_mauguin': 'Icma', 'hermann_mauguin_u': 'Icma', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Icma', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y-1/2,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Icma'}, {'hall': '-I 2b 2c', 'hermann_mauguin': 'Ibca', 'hermann_mauguin_u': 'Ibca', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2'], 'number': 73, 'point_group': 'mmm', 'schoenflies': 'D2h^27', 'short_h_m': 'Ibca', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1,-z+1', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Ibca'}, {'hall': '-I 2a 2b', 'hermann_mauguin': 'Icab', 'hermann_mauguin_u': 'Icab', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z'], 'number': 73, 'point_group': 'mmm', 'schoenflies': 'D2h^27', 'short_h_m': 'Icab', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x,y-1/2,z', 'x-1/2,-y-1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1,-y+1/2,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x+1,y+1,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Icab'}, {'hall': '-I 2b 2', 'hermann_mauguin': 'Imma', 'hermann_mauguin_u': 'Imma', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Imma', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z', 'x,-y-1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Imma'}, {'hall': '-I 2a 2a', 'hermann_mauguin': 'Immb', 'hermann_mauguin_u': 'Immb', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Immb', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x-1/2,y,-z', '-x-1/2,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1,-y+1/2,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Immb'}, {'hall': '-I 2c 2c', 'hermann_mauguin': 'Ibmm', 'hermann_mauguin_u': 'Ibmm', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Ibmm', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z+1/2', '-x,y,-z', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z-1/2', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Ibmm'}, {'hall': '-I 2 2b', 'hermann_mauguin': 'Icmm', 'hermann_mauguin_u': 'Icmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Icmm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y,-z', '-x,y-1/2,z', 'x,-y-1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1,-z+1/2', '-x+1/2,y+1,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Icmm'}, {'hall': '-I 2 2a', 'hermann_mauguin': 'Imcm', 'hermann_mauguin_u': 'Imcm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Imcm', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y,-z', '-x-1/2,y,z', 'x-1/2,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1,-y+1/2,-z+1/2', '-x+1,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Imcm'}, {'hall': '-I 2c 2', 'hermann_mauguin': 'Imam', 'hermann_mauguin_u': 'Imam', 'ncsym': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2'], 'number': 74, 'point_group': 'mmm', 'schoenflies': 'D2h^28', 'short_h_m': 'Imam', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x,-y,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z-1/2', '-x,y,z', 'x,-y,z-1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Imam'}, {'hall': ' P 4', 'hermann_mauguin': 'P4', 'hermann_mauguin_u': 'P4', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z'], 'number': 75, 'point_group': '4', 'schoenflies': 'C4^1', 'short_h_m': 'P4', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z'], 'universal_h_m': 'P4'}, {'hall': ' P 4w', 'hermann_mauguin': 'P41', 'hermann_mauguin_u': 'P4_1', 'ncsym': ['x,y,z', '-y,x,z+1/4', '-x,-y,z+1/2', 'y,-x,z+3/4'], 'number': 76, 'point_group': '4', 'schoenflies': 'C4^2', 'short_h_m': 'P4_1', 'symops': ['x,y,z', '-y,x,z+1/4', '-x,-y,z+1/2', 'y,-x,z+3/4'], 'universal_h_m': 'P41'}, {'hall': ' P 4c', 'hermann_mauguin': 'P42', 'hermann_mauguin_u': 'P4_2', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2'], 'number': 77, 'point_group': '4', 'schoenflies': 'C4^3', 'short_h_m': 'P4_2', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2'], 'universal_h_m': 'P42'}, {'hall': ' P 4cw', 'hermann_mauguin': 'P43', 'hermann_mauguin_u': 'P4_3', 'ncsym': ['x,y,z', '-y,x,z+3/4', '-x,-y,z+1/2', 'y,-x,z+1/4'], 'number': 78, 'point_group': '4', 'schoenflies': 'C4^4', 'short_h_m': 'P4_3', 'symops': ['x,y,z', '-y,x,z+3/4', '-x,-y,z+1/2', 'y,-x,z+1/4'], 'universal_h_m': 'P43'}, {'hall': ' I 4', 'hermann_mauguin': 'I4', 'hermann_mauguin_u': 'I4', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z'], 'number': 79, 'point_group': '4', 'schoenflies': 'C4^5', 'short_h_m': 'I4', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2'], 'universal_h_m': 'I4'}, {'hall': ' I 4bw', 'hermann_mauguin': 'I41', 'hermann_mauguin_u': 'I4_1', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4'], 'number': 80, 'point_group': '4', 'schoenflies': 'C4^6', 'short_h_m': 'I4_1', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4'], 'universal_h_m': 'I41'}, {'hall': ' P -4', 'hermann_mauguin': 'P-4', 'hermann_mauguin_u': 'P-4', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z'], 'number': 81, 'point_group': '-4', 'schoenflies': 'S4^1', 'short_h_m': 'P-4', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z'], 'universal_h_m': 'P-4'}, {'hall': ' I -4', 'hermann_mauguin': 'I-4', 'hermann_mauguin_u': 'I-4', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z'], 'number': 82, 'point_group': '-4', 'schoenflies': 'S4^2', 'short_h_m': 'I-4', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2'], 'universal_h_m': 'I-4'}, {'hall': '-P 4', 'hermann_mauguin': 'P4/m', 'hermann_mauguin_u': 'P4/m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z'], 'number': 83, 'point_group': '4/m', 'schoenflies': 'C4h^1', 'short_h_m': 'P4/m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z'], 'universal_h_m': 'P4/m'}, {'hall': '-P 4c', 'hermann_mauguin': 'P42/m', 'hermann_mauguin_u': 'P4_2/m', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2'], 'number': 84, 'point_group': '4/m', 'schoenflies': 'C4h^2', 'short_h_m': 'P4_2/m', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2'], 'universal_h_m': 'P42/m'}, {'hall': ' P 4ab -1ab', 'hermann_mauguin': 'P4/n', 'hermann_mauguin_u': 'P4/n', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z'], 'number': 85, 'point_group': '4/m', 'schoenflies': 'C4h^3', 'short_h_m': 'P4/n', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z'], 'universal_h_m': 'P4/n:1'}, {'hall': '-P 4a', 'hermann_mauguin': 'P4/n', 'hermann_mauguin_u': 'P4/n', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z'], 'number': 85, 'point_group': '4/m', 'schoenflies': 'C4h^3', 'short_h_m': 'P4/n', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z'], 'universal_h_m': 'P4/n:2'}, {'hall': ' P 4n -1n', 'hermann_mauguin': 'P42/n', 'hermann_mauguin_u': 'P4_2/n', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z'], 'number': 86, 'point_group': '4/m', 'schoenflies': 'C4h^4', 'short_h_m': 'P4_2/n', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z'], 'universal_h_m': 'P42/n:1'}, {'hall': '-P 4bc', 'hermann_mauguin': 'P42/n', 'hermann_mauguin_u': 'P4_2/n', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z+1/2', '-x,-y,-z', 'y,-x-1/2,-z-1/2', 'x-1/2,y-1/2,-z', '-y-1/2,x,-z-1/2'], 'number': 86, 'point_group': '4/m', 'schoenflies': 'C4h^4', 'short_h_m': 'P4_2/n', 'symops': ['x,y,z', '-y,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z+1/2', '-x,-y,-z', 'y,-x-1/2,-z-1/2', 'x-1/2,y-1/2,-z', '-y-1/2,x,-z-1/2'], 'universal_h_m': 'P42/n:2'}, {'hall': '-I 4', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2'], 'universal_h_m': 'I4/m'}, {'hall': ' I 4bw -1bw', 'hermann_mauguin': 'I41/a', 'hermann_mauguin_u': 'I4_1/a', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2'], 'number': 88, 'point_group': '4/m', 'schoenflies': 'C4h^6', 'short_h_m': 'I4_1/a', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', '-x+1/2,-y+1,-z+3/4', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/4', '-y,x+1,-z'], 'universal_h_m': 'I41/a:1'}, {'hall': '-I 4ad', 'hermann_mauguin': 'I41/a', 'hermann_mauguin_u': 'I4_1/a', 'ncsym': ['x,y,z', '-y+3/4,x+1/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+3/4,-x+3/4,z+3/4', '-x,-y,-z', 'y-3/4,-x-1/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-3/4,x-3/4,-z-3/4'], 'number': 88, 'point_group': '4/m', 'schoenflies': 'C4h^6', 'short_h_m': 'I4_1/a', 'symops': ['x,y,z', '-y+3/4,x+1/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+3/4,-x+3/4,z+3/4', '-x,-y,-z', 'y-3/4,-x-1/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-3/4,x-3/4,-z-3/4', 'x+1/2,y+1/2,z+1/2', '-y+5/4,x+3/4,z+3/4', '-x+1,-y+1/2,z+1', 'y+5/4,-x+5/4,z+5/4', '-x+1/2,-y+1/2,-z+1/2', 'y-1/4,-x+1/4,-z+1/4', 'x,y+1/2,-z', '-y-1/4,x-1/4,-z-1/4'], 'universal_h_m': 'I41/a:2'}, {'hall': ' P 4 2', 'hermann_mauguin': 'P422', 'hermann_mauguin_u': 'P422', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z'], 'number': 89, 'point_group': '422', 'schoenflies': 'D4^1', 'short_h_m': 'P422', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z'], 'universal_h_m': 'P422'}, {'hall': ' P 4ab 2ab', 'hermann_mauguin': 'P4212', 'hermann_mauguin_u': 'P42_12', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z'], 'number': 90, 'point_group': '422', 'schoenflies': 'D4^2', 'short_h_m': 'P42_12', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z'], 'universal_h_m': 'P4212'}, {'hall': ' P 4w 2c', 'hermann_mauguin': 'P4122', 'hermann_mauguin_u': 'P4_122', 'ncsym': ['x,y,z', '-y,x,z+1/4', '-x,-y,z+1/2', 'y,-x,z+3/4', 'x,-y,-z+1/2', 'y,x,-z+3/4', '-x,y,-z', '-y,-x,-z+1/4'], 'number': 91, 'point_group': '422', 'schoenflies': 'D4^3', 'short_h_m': 'P4_122', 'symops': ['x,y,z', '-y,x,z+1/4', '-x,-y,z+1/2', 'y,-x,z+3/4', 'x,-y,-z+1/2', 'y,x,-z+3/4', '-x,y,-z', '-y,-x,-z+1/4'], 'universal_h_m': 'P4122'}, {'hall': ' P 4abw 2nw', 'hermann_mauguin': 'P41212', 'hermann_mauguin_u': 'P4_12_12', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/4', '-x,-y,z+1/2', 'y+1/2,-x+1/2,z+3/4', 'x+1/2,-y+1/2,-z+3/4', 'y,x,-z', '-x+1/2,y+1/2,-z+1/4', '-y,-x,-z+1/2'], 'number': 92, 'point_group': '422', 'schoenflies': 'D4^4', 'short_h_m': 'P4_12_12', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/4', '-x,-y,z+1/2', 'y+1/2,-x+1/2,z+3/4', 'x+1/2,-y+1/2,-z+3/4', 'y,x,-z', '-x+1/2,y+1/2,-z+1/4', '-y,-x,-z+1/2'], 'universal_h_m': 'P41212'}, {'hall': ' P 4c 2', 'hermann_mauguin': 'P4222', 'hermann_mauguin_u': 'P4_222', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2'], 'number': 93, 'point_group': '422', 'schoenflies': 'D4^5', 'short_h_m': 'P4_222', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2'], 'universal_h_m': 'P4222'}, {'hall': ' P 4n 2n', 'hermann_mauguin': 'P42212', 'hermann_mauguin_u': 'P4_22_12', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z'], 'number': 94, 'point_group': '422', 'schoenflies': 'D4^6', 'short_h_m': 'P4_22_12', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z'], 'universal_h_m': 'P42212'}, {'hall': ' P 4cw 2c', 'hermann_mauguin': 'P4322', 'hermann_mauguin_u': 'P4_322', 'ncsym': ['x,y,z', '-y,x,z+3/4', '-x,-y,z+1/2', 'y,-x,z+1/4', 'x,-y,-z+1/2', 'y,x,-z+1/4', '-x,y,-z', '-y,-x,-z+3/4'], 'number': 95, 'point_group': '422', 'schoenflies': 'D4^7', 'short_h_m': 'P4_322', 'symops': ['x,y,z', '-y,x,z+3/4', '-x,-y,z+1/2', 'y,-x,z+1/4', 'x,-y,-z+1/2', 'y,x,-z+1/4', '-x,y,-z', '-y,-x,-z+3/4'], 'universal_h_m': 'P4322'}, {'hall': ' P 4nw 2abw', 'hermann_mauguin': 'P43212', 'hermann_mauguin_u': 'P4_32_12', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+3/4', '-x,-y,z+1/2', 'y+1/2,-x+1/2,z+1/4', 'x+1/2,-y+1/2,-z+1/4', 'y,x,-z', '-x+1/2,y+1/2,-z+3/4', '-y,-x,-z+1/2'], 'number': 96, 'point_group': '422', 'schoenflies': 'D4^8', 'short_h_m': 'P4_32_12', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+3/4', '-x,-y,z+1/2', 'y+1/2,-x+1/2,z+1/4', 'x+1/2,-y+1/2,-z+1/4', 'y,x,-z', '-x+1/2,y+1/2,-z+3/4', '-y,-x,-z+1/2'], 'universal_h_m': 'P43212'}, {'hall': ' I 4 2', 'hermann_mauguin': 'I422', 'hermann_mauguin_u': 'I422', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z'], 'number': 97, 'point_group': '422', 'schoenflies': 'D4^9', 'short_h_m': 'I422', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2'], 'universal_h_m': 'I422'}, {'hall': ' I 4bw 2bw', 'hermann_mauguin': 'I4122', 'hermann_mauguin_u': 'I4_122', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x,-y+1/2,-z+1/4', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+3/4', '-y,-x,-z'], 'number': 98, 'point_group': '422', 'schoenflies': 'D4^10', 'short_h_m': 'I4_122', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x,-y+1/2,-z+1/4', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+3/4', '-y,-x,-z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', 'x+1/2,-y+1,-z+3/4', 'y+1,x+1,-z+1', '-x+1,y+1/2,-z+5/4', '-y+1/2,-x+1/2,-z+1/2'], 'universal_h_m': 'I4122'}, {'hall': ' P 4 -2', 'hermann_mauguin': 'P4mm', 'hermann_mauguin_u': 'P4mm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 99, 'point_group': '4mm', 'schoenflies': 'C4v^1', 'short_h_m': 'P4mm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'universal_h_m': 'P4mm'}, {'hall': ' P 4 -2ab', 'hermann_mauguin': 'P4bm', 'hermann_mauguin_u': 'P4bm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'number': 100, 'point_group': '4mm', 'schoenflies': 'C4v^2', 'short_h_m': 'P4bm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'P4bm'}, {'hall': ' P 4c -2c', 'hermann_mauguin': 'P42cm', 'hermann_mauguin_u': 'P4_2cm', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'y,x,z'], 'number': 101, 'point_group': '4mm', 'schoenflies': 'C4v^3', 'short_h_m': 'P4_2cm', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'y,x,z'], 'universal_h_m': 'P42cm'}, {'hall': ' P 4n -2n', 'hermann_mauguin': 'P42nm', 'hermann_mauguin_u': 'P4_2nm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'number': 102, 'point_group': '4mm', 'schoenflies': 'C4v^4', 'short_h_m': 'P4_2nm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'universal_h_m': 'P42nm'}, {'hall': ' P 4 -2c', 'hermann_mauguin': 'P4cc', 'hermann_mauguin_u': 'P4cc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2'], 'number': 103, 'point_group': '4mm', 'schoenflies': 'C4v^5', 'short_h_m': 'P4cc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2'], 'universal_h_m': 'P4cc'}, {'hall': ' P 4 -2n', 'hermann_mauguin': 'P4nc', 'hermann_mauguin_u': 'P4nc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 104, 'point_group': '4mm', 'schoenflies': 'C4v^6', 'short_h_m': 'P4nc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P4nc'}, {'hall': ' P 4c -2', 'hermann_mauguin': 'P42mc', 'hermann_mauguin_u': 'P4_2mc', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'y,x,z+1/2'], 'number': 105, 'point_group': '4mm', 'schoenflies': 'C4v^7', 'short_h_m': 'P4_2mc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'y,x,z+1/2'], 'universal_h_m': 'P42mc'}, {'hall': ' P 4c -2ab', 'hermann_mauguin': 'P42bc', 'hermann_mauguin_u': 'P4_2bc', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z+1/2'], 'number': 106, 'point_group': '4mm', 'schoenflies': 'C4v^8', 'short_h_m': 'P4_2bc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P42bc'}, {'hall': ' I 4 -2', 'hermann_mauguin': 'I4mm', 'hermann_mauguin_u': 'I4mm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 107, 'point_group': '4mm', 'schoenflies': 'C4v^9', 'short_h_m': 'I4mm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'I4mm'}, {'hall': ' I 4 -2c', 'hermann_mauguin': 'I4cm', 'hermann_mauguin_u': 'I4cm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2'], 'number': 108, 'point_group': '4mm', 'schoenflies': 'C4v^10', 'short_h_m': 'I4cm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,z+1', '-y+1/2,-x+1/2,z+1', 'x+1/2,-y+1/2,z+1', 'y+1/2,x+1/2,z+1'], 'universal_h_m': 'I4cm'}, {'hall': ' I 4bw -2', 'hermann_mauguin': 'I41md', 'hermann_mauguin_u': 'I4_1md', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,y,z', '-y,-x+1/2,z+1/4', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x,z+3/4'], 'number': 109, 'point_group': '4mm', 'schoenflies': 'C4v^11', 'short_h_m': 'I4_1md', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,y,z', '-y,-x+1/2,z+1/4', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x,z+3/4', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1,z+3/4', 'x+1,-y+1,z+1', 'y+1,x+1/2,z+5/4'], 'universal_h_m': 'I41md'}, {'hall': ' I 4bw -2c', 'hermann_mauguin': 'I41cd', 'hermann_mauguin_u': 'I4_1cd', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,y,z+1/2', '-y,-x+1/2,z+3/4', 'x+1/2,-y+1/2,z', 'y+1/2,x,z+1/4'], 'number': 110, 'point_group': '4mm', 'schoenflies': 'C4v^12', 'short_h_m': 'I4_1cd', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', '-x,y,z+1/2', '-y,-x+1/2,z+3/4', 'x+1/2,-y+1/2,z', 'y+1/2,x,z+1/4', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', '-x+1/2,y+1/2,z+1', '-y+1/2,-x+1,z+5/4', 'x+1,-y+1,z+1/2', 'y+1,x+1/2,z+3/4'], 'universal_h_m': 'I41cd'}, {'hall': ' P -4 2', 'hermann_mauguin': 'P-42m', 'hermann_mauguin_u': 'P-42m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z'], 'number': 111, 'point_group': '-42m', 'schoenflies': 'D2d^1', 'short_h_m': 'P-42m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z'], 'universal_h_m': 'P-42m'}, {'hall': ' P -4 2c', 'hermann_mauguin': 'P-42c', 'hermann_mauguin_u': 'P-42c', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z+1/2', '-y,-x,z+1/2', '-x,y,-z+1/2', 'y,x,z+1/2'], 'number': 112, 'point_group': '-42m', 'schoenflies': 'D2d^2', 'short_h_m': 'P-42c', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z+1/2', '-y,-x,z+1/2', '-x,y,-z+1/2', 'y,x,z+1/2'], 'universal_h_m': 'P-42c'}, {'hall': ' P -4 2ab', 'hermann_mauguin': 'P-421m', 'hermann_mauguin_u': 'P-42_1m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x+1/2,-y+1/2,-z', '-y+1/2,-x+1/2,z', '-x+1/2,y+1/2,-z', 'y+1/2,x+1/2,z'], 'number': 113, 'point_group': '-42m', 'schoenflies': 'D2d^3', 'short_h_m': 'P-42_1m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x+1/2,-y+1/2,-z', '-y+1/2,-x+1/2,z', '-x+1/2,y+1/2,-z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'P-421m'}, {'hall': ' P -4 2n', 'hermann_mauguin': 'P-421c', 'hermann_mauguin_u': 'P-42_1c', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x+1/2,-y+1/2,-z+1/2', '-y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 114, 'point_group': '-42m', 'schoenflies': 'D2d^4', 'short_h_m': 'P-42_1c', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x+1/2,-y+1/2,-z+1/2', '-y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P-421c'}, {'hall': ' P -4 -2', 'hermann_mauguin': 'P-4m2', 'hermann_mauguin_u': 'P-4m2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z', 'y,x,-z', 'x,-y,z', '-y,-x,-z'], 'number': 115, 'point_group': '-42m', 'schoenflies': 'D2d^5', 'short_h_m': 'P-4m2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z', 'y,x,-z', 'x,-y,z', '-y,-x,-z'], 'universal_h_m': 'P-4m2'}, {'hall': ' P -4 -2c', 'hermann_mauguin': 'P-4c2', 'hermann_mauguin_u': 'P-4c2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z+1/2', 'y,x,-z+1/2', 'x,-y,z+1/2', '-y,-x,-z+1/2'], 'number': 116, 'point_group': '-42m', 'schoenflies': 'D2d^6', 'short_h_m': 'P-4c2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z+1/2', 'y,x,-z+1/2', 'x,-y,z+1/2', '-y,-x,-z+1/2'], 'universal_h_m': 'P-4c2'}, {'hall': ' P -4 -2ab', 'hermann_mauguin': 'P-4b2', 'hermann_mauguin_u': 'P-4b2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x+1/2,y+1/2,z', 'y+1/2,x+1/2,-z', 'x+1/2,-y+1/2,z', '-y+1/2,-x+1/2,-z'], 'number': 117, 'point_group': '-42m', 'schoenflies': 'D2d^7', 'short_h_m': 'P-4b2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x+1/2,y+1/2,z', 'y+1/2,x+1/2,-z', 'x+1/2,-y+1/2,z', '-y+1/2,-x+1/2,-z'], 'universal_h_m': 'P-4b2'}, {'hall': ' P -4 -2n', 'hermann_mauguin': 'P-4n2', 'hermann_mauguin_u': 'P-4n2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', 'y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2'], 'number': 118, 'point_group': '-42m', 'schoenflies': 'D2d^8', 'short_h_m': 'P-4n2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', 'y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2'], 'universal_h_m': 'P-4n2'}, {'hall': ' I -4 -2', 'hermann_mauguin': 'I-4m2', 'hermann_mauguin_u': 'I-4m2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z', 'y,x,-z', 'x,-y,z', '-y,-x,-z'], 'number': 119, 'point_group': '-42m', 'schoenflies': 'D2d^9', 'short_h_m': 'I-4m2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z', 'y,x,-z', 'x,-y,z', '-y,-x,-z', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2'], 'universal_h_m': 'I-4m2'}, {'hall': ' I -4 -2c', 'hermann_mauguin': 'I-4c2', 'hermann_mauguin_u': 'I-4c2', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z+1/2', 'y,x,-z+1/2', 'x,-y,z+1/2', '-y,-x,-z+1/2'], 'number': 120, 'point_group': '-42m', 'schoenflies': 'D2d^10', 'short_h_m': 'I-4c2', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', '-x,y,z+1/2', 'y,x,-z+1/2', 'x,-y,z+1/2', '-y,-x,-z+1/2', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1', 'y+1/2,x+1/2,-z+1', 'x+1/2,-y+1/2,z+1', '-y+1/2,-x+1/2,-z+1'], 'universal_h_m': 'I-4c2'}, {'hall': ' I -4 2', 'hermann_mauguin': 'I-42m', 'hermann_mauguin_u': 'I-42m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z'], 'number': 121, 'point_group': '-42m', 'schoenflies': 'D2d^11', 'short_h_m': 'I-42m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'I-42m'}, {'hall': ' I -4 2bw', 'hermann_mauguin': 'I-42d', 'hermann_mauguin_u': 'I-42d', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y+1/2,-z+1/4', '-y+1/2,-x,z+3/4', '-x,y+1/2,-z+1/4', 'y+1/2,x,z+3/4'], 'number': 122, 'point_group': '-42m', 'schoenflies': 'D2d^12', 'short_h_m': 'I-42d', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y+1/2,-z+1/4', '-y+1/2,-x,z+3/4', '-x,y+1/2,-z+1/4', 'y+1/2,x,z+3/4', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1,-z+3/4', '-y+1,-x+1/2,z+5/4', '-x+1/2,y+1,-z+3/4', 'y+1,x+1/2,z+5/4'], 'universal_h_m': 'I-42d'}, {'hall': '-P 4 2', 'hermann_mauguin': 'P4/mmm', 'hermann_mauguin_u': 'P4/mmm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 123, 'point_group': '4/mmm', 'schoenflies': 'D4h^1', 'short_h_m': 'P4/mmm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'universal_h_m': 'P4/mmm'}, {'hall': '-P 4 2c', 'hermann_mauguin': 'P4/mcc', 'hermann_mauguin_u': 'P4/mcc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z-1/2', '-y,-x,z-1/2', 'x,-y,z-1/2', 'y,x,z-1/2'], 'number': 124, 'point_group': '4/mmm', 'schoenflies': 'D4h^2', 'short_h_m': 'P4/mcc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z-1/2', '-y,-x,z-1/2', 'x,-y,z-1/2', 'y,x,z-1/2'], 'universal_h_m': 'P4/mcc'}, {'hall': ' P 4 2 -1ab', 'hermann_mauguin': 'P4/nbm', 'hermann_mauguin_u': 'P4/nbm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'number': 125, 'point_group': '4/mmm', 'schoenflies': 'D4h^3', 'short_h_m': 'P4/nbm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'P4/nbm:1'}, {'hall': '-P 4a 2b', 'hermann_mauguin': 'P4/nbm', 'hermann_mauguin_u': 'P4/nbm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z', '-y,-x,z', 'x-1/2,-y,z', 'y-1/2,x-1/2,z'], 'number': 125, 'point_group': '4/mmm', 'schoenflies': 'D4h^3', 'short_h_m': 'P4/nbm', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z', '-y,-x,z', 'x-1/2,-y,z', 'y-1/2,x-1/2,z'], 'universal_h_m': 'P4/nbm:2'}, {'hall': ' P 4 2 -1n', 'hermann_mauguin': 'P4/nnc', 'hermann_mauguin_u': 'P4/nnc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 126, 'point_group': '4/mmm', 'schoenflies': 'D4h^4', 'short_h_m': 'P4/nnc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P4/nnc:1'}, {'hall': '-P 4a 2bc', 'hermann_mauguin': 'P4/nnc', 'hermann_mauguin_u': 'P4/nnc', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z-1/2', '-y,-x,z-1/2', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z-1/2'], 'number': 126, 'point_group': '4/mmm', 'schoenflies': 'D4h^4', 'short_h_m': 'P4/nnc', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z-1/2', '-y,-x,z-1/2', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z-1/2'], 'universal_h_m': 'P4/nnc:2'}, {'hall': '-P 4 2ab', 'hermann_mauguin': 'P4/mbm', 'hermann_mauguin_u': 'P4/mbm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x-1/2,y-1/2,z', '-y-1/2,-x-1/2,z', 'x-1/2,-y-1/2,z', 'y-1/2,x-1/2,z'], 'number': 127, 'point_group': '4/mmm', 'schoenflies': 'D4h^5', 'short_h_m': 'P4/mbm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x-1/2,y-1/2,z', '-y-1/2,-x-1/2,z', 'x-1/2,-y-1/2,z', 'y-1/2,x-1/2,z'], 'universal_h_m': 'P4/mbm'}, {'hall': '-P 4 2n', 'hermann_mauguin': 'P4/mnc', 'hermann_mauguin_u': 'P4/mnc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x-1/2,y-1/2,z-1/2', '-y-1/2,-x-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2', 'y-1/2,x-1/2,z-1/2'], 'number': 128, 'point_group': '4/mmm', 'schoenflies': 'D4h^6', 'short_h_m': 'P4/mnc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x-1/2,y-1/2,z-1/2', '-y-1/2,-x-1/2,z-1/2', 'x-1/2,-y-1/2,z-1/2', 'y-1/2,x-1/2,z-1/2'], 'universal_h_m': 'P4/mnc'}, {'hall': ' P 4ab 2ab -1ab', 'hermann_mauguin': 'P4/nmm', 'hermann_mauguin_u': 'P4/nmm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z', '-y+1/2,-x+1/2,z', 'x,-y,z', 'y+1/2,x+1/2,z'], 'number': 129, 'point_group': '4/mmm', 'schoenflies': 'D4h^7', 'short_h_m': 'P4/nmm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z', '-y+1/2,-x+1/2,z', 'x,-y,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'P4/nmm:1'}, {'hall': '-P 4a 2a', 'hermann_mauguin': 'P4/nmm', 'hermann_mauguin_u': 'P4/nmm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x-1/2,y,z', '-y-1/2,-x-1/2,z', 'x,-y-1/2,z', 'y,x,z'], 'number': 129, 'point_group': '4/mmm', 'schoenflies': 'D4h^7', 'short_h_m': 'P4/nmm', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x-1/2,y,z', '-y-1/2,-x-1/2,z', 'x,-y-1/2,z', 'y,x,z'], 'universal_h_m': 'P4/nmm:2'}, {'hall': ' P 4ab 2n -1ab', 'hermann_mauguin': 'P4/ncc', 'hermann_mauguin_u': 'P4/ncc', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z-1/2', '-y+1/2,-x+1/2,z-1/2', 'x,-y,z-1/2', 'y+1/2,x+1/2,z-1/2'], 'number': 130, 'point_group': '4/mmm', 'schoenflies': 'D4h^8', 'short_h_m': 'P4/ncc', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z-1/2', '-y+1/2,-x+1/2,z-1/2', 'x,-y,z-1/2', 'y+1/2,x+1/2,z-1/2'], 'universal_h_m': 'P4/ncc:1'}, {'hall': '-P 4a 2ac', 'hermann_mauguin': 'P4/ncc', 'hermann_mauguin_u': 'P4/ncc', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x-1/2,y,z-1/2', '-y-1/2,-x-1/2,z-1/2', 'x,-y-1/2,z-1/2', 'y,x,z-1/2'], 'number': 130, 'point_group': '4/mmm', 'schoenflies': 'D4h^8', 'short_h_m': 'P4/ncc', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x-1/2,y,z-1/2', '-y-1/2,-x-1/2,z-1/2', 'x,-y-1/2,z-1/2', 'y,x,z-1/2'], 'universal_h_m': 'P4/ncc:2'}, {'hall': '-P 4c 2', 'hermann_mauguin': 'P42/mmc', 'hermann_mauguin_u': 'P4_2/mmc', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x,y,z', '-y,-x,z-1/2', 'x,-y,z', 'y,x,z-1/2'], 'number': 131, 'point_group': '4/mmm', 'schoenflies': 'D4h^9', 'short_h_m': 'P4_2/mmc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x,y,z', '-y,-x,z-1/2', 'x,-y,z', 'y,x,z-1/2'], 'universal_h_m': 'P42/mmc'}, {'hall': '-P 4c 2c', 'hermann_mauguin': 'P42/mcm', 'hermann_mauguin_u': 'P4_2/mcm', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x,y,z-1/2', '-y,-x,z', 'x,-y,z-1/2', 'y,x,z'], 'number': 132, 'point_group': '4/mmm', 'schoenflies': 'D4h^10', 'short_h_m': 'P4_2/mcm', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x,y,z-1/2', '-y,-x,z', 'x,-y,z-1/2', 'y,x,z'], 'universal_h_m': 'P42/mcm'}, {'hall': ' P 4n 2c -1n', 'hermann_mauguin': 'P42/nbc', 'hermann_mauguin_u': 'P4_2/nbc', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z', 'y,x,z+1/2'], 'number': 133, 'point_group': '4/mmm', 'schoenflies': 'D4h^11', 'short_h_m': 'P4_2/nbc', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z', 'y,x,z+1/2'], 'universal_h_m': 'P42/nbc:1'}, {'hall': '-P 4ac 2b', 'hermann_mauguin': 'P42/nbc', 'hermann_mauguin_u': 'P4_2/nbc', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x,y-1/2,z', '-y,-x,z-1/2', 'x-1/2,-y,z', 'y-1/2,x-1/2,z-1/2'], 'number': 133, 'point_group': '4/mmm', 'schoenflies': 'D4h^11', 'short_h_m': 'P4_2/nbc', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x,y-1/2,z', '-y,-x,z-1/2', 'x-1/2,-y,z', 'y-1/2,x-1/2,z-1/2'], 'universal_h_m': 'P42/nbc:2'}, {'hall': ' P 4n 2 -1n', 'hermann_mauguin': 'P42/nnm', 'hermann_mauguin_u': 'P4_2/nnm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'number': 134, 'point_group': '4/mmm', 'schoenflies': 'D4h^12', 'short_h_m': 'P4_2/nnm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'universal_h_m': 'P42/nnm:1'}, {'hall': '-P 4ac 2bc', 'hermann_mauguin': 'P42/nnm', 'hermann_mauguin_u': 'P4_2/nnm', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x,y-1/2,z-1/2', '-y,-x,z', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z'], 'number': 134, 'point_group': '4/mmm', 'schoenflies': 'D4h^12', 'short_h_m': 'P4_2/nnm', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x,y-1/2,z-1/2', '-y,-x,z', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z'], 'universal_h_m': 'P42/nnm:2'}, {'hall': '-P 4c 2ab', 'hermann_mauguin': 'P42/mbc', 'hermann_mauguin_u': 'P4_2/mbc', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x-1/2,y-1/2,z', '-y-1/2,-x-1/2,z-1/2', 'x-1/2,-y-1/2,z', 'y-1/2,x-1/2,z-1/2'], 'number': 135, 'point_group': '4/mmm', 'schoenflies': 'D4h^13', 'short_h_m': 'P4_2/mbc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y,-x,-z-1/2', 'x,y,-z', '-y,x,-z-1/2', '-x-1/2,y-1/2,z', '-y-1/2,-x-1/2,z-1/2', 'x-1/2,-y-1/2,z', 'y-1/2,x-1/2,z-1/2'], 'universal_h_m': 'P42/mbc'}, {'hall': '-P 4n 2n', 'hermann_mauguin': 'P42/mnm', 'hermann_mauguin_u': 'P4_2/mnm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x-1/2,-z-1/2', 'x,y,-z', '-y-1/2,x-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', '-y,-x,z', 'x-1/2,-y-1/2,z-1/2', 'y,x,z'], 'number': 136, 'point_group': '4/mmm', 'schoenflies': 'D4h^14', 'short_h_m': 'P4_2/mnm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x-1/2,-z-1/2', 'x,y,-z', '-y-1/2,x-1/2,-z-1/2', '-x-1/2,y-1/2,z-1/2', '-y,-x,z', 'x-1/2,-y-1/2,z-1/2', 'y,x,z'], 'universal_h_m': 'P42/mnm'}, {'hall': ' P 4n 2n -1n', 'hermann_mauguin': 'P42/nmc', 'hermann_mauguin_u': 'P4_2/nmc', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x,y,z', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z', 'y+1/2,x+1/2,z+1/2'], 'number': 137, 'point_group': '4/mmm', 'schoenflies': 'D4h^15', 'short_h_m': 'P4_2/nmc', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x,y,z', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P42/nmc:1'}, {'hall': '-P 4ac 2a', 'hermann_mauguin': 'P42/nmc', 'hermann_mauguin_u': 'P4_2/nmc', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x-1/2,y,z', '-y-1/2,-x-1/2,z-1/2', 'x,-y-1/2,z', 'y,x,z-1/2'], 'number': 137, 'point_group': '4/mmm', 'schoenflies': 'D4h^15', 'short_h_m': 'P4_2/nmc', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x-1/2,y,z', '-y-1/2,-x-1/2,z-1/2', 'x,-y-1/2,z', 'y,x,z-1/2'], 'universal_h_m': 'P42/nmc:2'}, {'hall': ' P 4n 2ab -1n', 'hermann_mauguin': 'P42/ncm', 'hermann_mauguin_u': 'P4_2/ncm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x,y,z+1/2', '-y+1/2,-x+1/2,z', 'x,-y,z+1/2', 'y+1/2,x+1/2,z'], 'number': 138, 'point_group': '4/mmm', 'schoenflies': 'D4h^16', 'short_h_m': 'P4_2/ncm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x,y,z+1/2', '-y+1/2,-x+1/2,z', 'x,-y,z+1/2', 'y+1/2,x+1/2,z'], 'universal_h_m': 'P42/ncm:1'}, {'hall': '-P 4ac 2ac', 'hermann_mauguin': 'P42/ncm', 'hermann_mauguin_u': 'P4_2/ncm', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x-1/2,y,z-1/2', '-y-1/2,-x-1/2,z', 'x,-y-1/2,z-1/2', 'y,x,z'], 'number': 138, 'point_group': '4/mmm', 'schoenflies': 'D4h^16', 'short_h_m': 'P4_2/ncm', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y-1/2,-x,-z-1/2', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z-1/2', '-x-1/2,y,z-1/2', '-y-1/2,-x-1/2,z', 'x,-y-1/2,z-1/2', 'y,x,z'], 'universal_h_m': 'P42/ncm:2'}, {'hall': '-I 4 2', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'I4/mmm'}, {'hall': '-I 4 2c', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z-1/2', '-y,-x,z-1/2', 'x,-y,z-1/2', 'y,x,z-1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z-1/2', '-y,-x,z-1/2', 'x,-y,z-1/2', 'y,x,z-1/2', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1', 'y+1/2,x+1/2,-z+1', '-x+1/2,y+1/2,-z+1', '-y+1/2,-x+1/2,-z+1', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'I4/mcm'}, {'hall': ' I 4bw 2bw -1bw', 'hermann_mauguin': 'I41/amd', 'hermann_mauguin_u': 'I4_1/amd', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x,-y+1/2,-z+1/4', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+3/4', '-y,-x,-z', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2', '-x,y,z', '-y-1/2,-x,z-1/4', 'x-1/2,-y+1/2,z-1/2', 'y,x+1/2,z+1/4'], 'number': 141, 'point_group': '4/mmm', 'schoenflies': 'D4h^19', 'short_h_m': 'I4_1/amd', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x,-y+1/2,-z+1/4', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+3/4', '-y,-x,-z', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2', '-x,y,z', '-y-1/2,-x,z-1/4', 'x-1/2,-y+1/2,z-1/2', 'y,x+1/2,z+1/4', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', 'x+1/2,-y+1,-z+3/4', 'y+1,x+1,-z+1', '-x+1,y+1/2,-z+5/4', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1,-z+3/4', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/4', '-y,x+1,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x+1/2,z+1/4', 'x,-y+1,z', 'y+1/2,x+1,z+3/4'], 'universal_h_m': 'I41/amd:1'}, {'hall': '-I 4bd 2', 'hermann_mauguin': 'I41/amd', 'hermann_mauguin_u': 'I4_1/amd', 'ncsym': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+3/4,-z+1/4', '-x+1/2,y,-z+1/2', '-y+1/4,-x+1/4,-z+3/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z', '-y-1/4,-x-3/4,z-1/4', 'x-1/2,-y,z-1/2', 'y-1/4,x-1/4,z-3/4'], 'number': 141, 'point_group': '4/mmm', 'schoenflies': 'D4h^19', 'short_h_m': 'I4_1/amd', 'symops': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+3/4,-z+1/4', '-x+1/2,y,-z+1/2', '-y+1/4,-x+1/4,-z+3/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z', '-y-1/4,-x-3/4,z-1/4', 'x-1/2,-y,z-1/2', 'y-1/4,x-1/4,z-3/4', 'x+1/2,y+1/2,z+1/2', '-y+3/4,x+5/4,z+3/4', '-x+1,-y+1/2,z+1', 'y+3/4,-x+3/4,z+5/4', 'x+1/2,-y+1/2,-z+1/2', 'y+3/4,x+5/4,-z+3/4', '-x+1,y+1/2,-z+1', '-y+3/4,-x+3/4,-z+5/4', '-x+1/2,-y+1/2,-z+1/2', 'y+1/4,-x-1/4,-z+1/4', 'x,y+1/2,-z', '-y+1/4,x+1/4,-z-1/4', '-x+1/2,y+1/2,z+1/2', '-y+1/4,-x-1/4,z+1/4', 'x,-y+1/2,z', 'y+1/4,x+1/4,z-1/4'], 'universal_h_m': 'I41/amd:2'}, {'hall': ' I 4bw 2aw -1bw', 'hermann_mauguin': 'I41/acd', 'hermann_mauguin_u': 'I4_1/acd', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x+1/2,-y,-z+1/4', 'y,x,-z+1/2', '-x,y+1/2,-z+3/4', '-y+1/2,-x+1/2,-z', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2', '-x-1/2,y+1/2,z', '-y,-x+1/2,z-1/4', 'x,-y,z-1/2', 'y-1/2,x,z+1/4'], 'number': 142, 'point_group': '4/mmm', 'schoenflies': 'D4h^20', 'short_h_m': 'I4_1/acd', 'symops': ['x,y,z', '-y,x+1/2,z+1/4', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x,z+3/4', 'x+1/2,-y,-z+1/4', 'y,x,-z+1/2', '-x,y+1/2,-z+3/4', '-y+1/2,-x+1/2,-z', '-x,-y+1/2,-z+1/4', 'y,-x,-z', 'x-1/2,y,-z-1/4', '-y-1/2,x+1/2,-z-1/2', '-x-1/2,y+1/2,z', '-y,-x+1/2,z-1/4', 'x,-y,z-1/2', 'y-1/2,x,z+1/4', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1,z+3/4', '-x+1,-y+1,z+1', 'y+1,-x+1/2,z+5/4', 'x+1,-y+1/2,-z+3/4', 'y+1/2,x+1/2,-z+1', '-x+1/2,y+1,-z+5/4', '-y+1,-x+1,-z+1/2', '-x+1/2,-y+1,-z+3/4', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/4', '-y,x+1,-z', '-x,y+1,z+1/2', '-y+1/2,-x+1,z+1/4', 'x+1/2,-y+1/2,z', 'y,x+1/2,z+3/4'], 'universal_h_m': 'I41/acd:1'}, {'hall': '-I 4bd 2c', 'hermann_mauguin': 'I41/acd', 'hermann_mauguin_u': 'I4_1/acd', 'ncsym': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z-1/2', '-y-1/4,-x-3/4,z-3/4', 'x-1/2,-y,z', 'y-1/4,x-1/4,z-1/4'], 'number': 142, 'point_group': '4/mmm', 'schoenflies': 'D4h^20', 'short_h_m': 'I4_1/acd', 'symops': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z-1/2', '-y-1/4,-x-3/4,z-3/4', 'x-1/2,-y,z', 'y-1/4,x-1/4,z-1/4', 'x+1/2,y+1/2,z+1/2', '-y+3/4,x+5/4,z+3/4', '-x+1,-y+1/2,z+1', 'y+3/4,-x+3/4,z+5/4', 'x+1/2,-y+1/2,-z+1', 'y+3/4,x+5/4,-z+5/4', '-x+1,y+1/2,-z+1/2', '-y+3/4,-x+3/4,-z+3/4', '-x+1/2,-y+1/2,-z+1/2', 'y+1/4,-x-1/4,-z+1/4', 'x,y+1/2,-z', '-y+1/4,x+1/4,-z-1/4', '-x+1/2,y+1/2,z', '-y+1/4,-x-1/4,z-1/4', 'x,-y+1/2,z+1/2', 'y+1/4,x+1/4,z+1/4'], 'universal_h_m': 'I41/acd:2'}, {'hall': ' P 3', 'hermann_mauguin': 'P3', 'hermann_mauguin_u': 'P3', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z'], 'number': 143, 'point_group': '3', 'schoenflies': 'C3^1', 'short_h_m': 'P3', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z'], 'universal_h_m': 'P3'}, {'hall': ' P 31', 'hermann_mauguin': 'P31', 'hermann_mauguin_u': 'P3_1', 'ncsym': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3'], 'number': 144, 'point_group': '3', 'schoenflies': 'C3^2', 'short_h_m': 'P3_1', 'symops': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3'], 'universal_h_m': 'P31'}, {'hall': ' P 32', 'hermann_mauguin': 'P32', 'hermann_mauguin_u': 'P3_2', 'ncsym': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3'], 'number': 145, 'point_group': '3', 'schoenflies': 'C3^3', 'short_h_m': 'P3_2', 'symops': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3'], 'universal_h_m': 'P32'}, {'hall': ' R 3', 'hermann_mauguin': 'R3', 'hermann_mauguin_u': 'R3', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z'], 'number': 146, 'point_group': '3', 'schoenflies': 'C3^4', 'short_h_m': 'R3', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3'], 'universal_h_m': 'R3:H'}, {'hall': ' P 3*', 'hermann_mauguin': 'R3', 'hermann_mauguin_u': 'R3', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x'], 'number': 146, 'point_group': '3', 'schoenflies': 'C3^4', 'short_h_m': 'R3', 'symops': ['x,y,z', 'z,x,y', 'y,z,x'], 'universal_h_m': 'R3:R'}, {'hall': '-P 3', 'hermann_mauguin': 'P-3', 'hermann_mauguin_u': 'P-3', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z'], 'number': 147, 'point_group': '-3', 'schoenflies': 'C3i^1', 'short_h_m': 'P-3', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z'], 'universal_h_m': 'P-3'}, {'hall': '-R 3', 'hermann_mauguin': 'R-3', 'hermann_mauguin_u': 'R-3', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z'], 'number': 148, 'point_group': '-3', 'schoenflies': 'C3i^2', 'short_h_m': 'R-3', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', '-x+2/3,-y+1/3,-z+1/3', 'y+2/3,-x+y+1/3,-z+1/3', 'x-y+2/3,x+1/3,-z+1/3', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', '-x+1/3,-y+2/3,-z+2/3', 'y+1/3,-x+y+2/3,-z+2/3', 'x-y+1/3,x+2/3,-z+2/3'], 'universal_h_m': 'R-3:H'}, {'hall': '-P 3*', 'hermann_mauguin': 'R-3', 'hermann_mauguin_u': 'R-3', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x'], 'number': 148, 'point_group': '-3', 'schoenflies': 'C3i^2', 'short_h_m': 'R-3', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x'], 'universal_h_m': 'R-3:R'}, {'hall': ' P 3 2', 'hermann_mauguin': 'P312', 'hermann_mauguin_u': 'P312', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z', 'x,x-y,-z', '-x+y,y,-z'], 'number': 149, 'point_group': '32', 'schoenflies': 'D3^1', 'short_h_m': 'P312', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z', 'x,x-y,-z', '-x+y,y,-z'], 'universal_h_m': 'P312'}, {'hall': ' P 3 2"', 'hermann_mauguin': 'P321', 'hermann_mauguin_u': 'P321', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z'], 'number': 150, 'point_group': '32', 'schoenflies': 'D3^2', 'short_h_m': 'P321', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z'], 'universal_h_m': 'P321'}, {'hall': ' P 31 2 (0 0 4)', 'hermann_mauguin': 'P3112', 'hermann_mauguin_u': 'P3_112', 'ncsym': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3', '-y,-x,-z+2/3', 'x,x-y,-z', '-x+y,y,-z+1/3'], 'number': 151, 'point_group': '32', 'schoenflies': 'D3^3', 'short_h_m': 'P3_112', 'symops': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3', '-y,-x,-z+2/3', 'x,x-y,-z', '-x+y,y,-z+1/3'], 'universal_h_m': 'P3112'}, {'hall': ' P 31 2"', 'hermann_mauguin': 'P3121', 'hermann_mauguin_u': 'P3_121', 'ncsym': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3', 'y,x,-z', '-x,-x+y,-z+1/3', 'x-y,-y,-z+2/3'], 'number': 152, 'point_group': '32', 'schoenflies': 'D3^4', 'short_h_m': 'P3_121', 'symops': ['x,y,z', '-y,x-y,z+1/3', '-x+y,-x,z+2/3', 'y,x,-z', '-x,-x+y,-z+1/3', 'x-y,-y,-z+2/3'], 'universal_h_m': 'P3121'}, {'hall': ' P 32 2 (0 0 2)', 'hermann_mauguin': 'P3212', 'hermann_mauguin_u': 'P3_212', 'ncsym': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3', '-y,-x,-z+1/3', 'x,x-y,-z', '-x+y,y,-z+2/3'], 'number': 153, 'point_group': '32', 'schoenflies': 'D3^5', 'short_h_m': 'P3_212', 'symops': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3', '-y,-x,-z+1/3', 'x,x-y,-z', '-x+y,y,-z+2/3'], 'universal_h_m': 'P3212'}, {'hall': ' P 32 2"', 'hermann_mauguin': 'P3221', 'hermann_mauguin_u': 'P3_221', 'ncsym': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3', 'y,x,-z', '-x,-x+y,-z+2/3', 'x-y,-y,-z+1/3'], 'number': 154, 'point_group': '32', 'schoenflies': 'D3^6', 'short_h_m': 'P3_221', 'symops': ['x,y,z', '-y,x-y,z+2/3', '-x+y,-x,z+1/3', 'y,x,-z', '-x,-x+y,-z+2/3', 'x-y,-y,-z+1/3'], 'universal_h_m': 'P3221'}, {'hall': ' R 3 2"', 'hermann_mauguin': 'R32', 'hermann_mauguin_u': 'R32', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z'], 'number': 155, 'point_group': '32', 'schoenflies': 'D3^7', 'short_h_m': 'R32', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', 'y+2/3,x+1/3,-z+1/3', '-x+2/3,-x+y+1/3,-z+1/3', 'x-y+2/3,-y+1/3,-z+1/3', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', 'y+1/3,x+2/3,-z+2/3', '-x+1/3,-x+y+2/3,-z+2/3', 'x-y+1/3,-y+2/3,-z+2/3'], 'universal_h_m': 'R32:H'}, {'hall': ' P 3* 2', 'hermann_mauguin': 'R32', 'hermann_mauguin_u': 'R32', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', '-y,-x,-z', '-z,-y,-x', '-x,-z,-y'], 'number': 155, 'point_group': '32', 'schoenflies': 'D3^7', 'short_h_m': 'R32', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', '-y,-x,-z', '-z,-y,-x', '-x,-z,-y'], 'universal_h_m': 'R32:R'}, {'hall': ' P 3 -2"', 'hermann_mauguin': 'P3m1', 'hermann_mauguin_u': 'P3m1', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'number': 156, 'point_group': '3m', 'schoenflies': 'C3v^1', 'short_h_m': 'P3m1', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'universal_h_m': 'P3m1'}, {'hall': ' P 3 -2', 'hermann_mauguin': 'P31m', 'hermann_mauguin_u': 'P31m', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,z', '-x,-x+y,z', 'x-y,-y,z'], 'number': 157, 'point_group': '3m', 'schoenflies': 'C3v^2', 'short_h_m': 'P31m', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,z', '-x,-x+y,z', 'x-y,-y,z'], 'universal_h_m': 'P31m'}, {'hall': ' P 3 -2"c', 'hermann_mauguin': 'P3c1', 'hermann_mauguin_u': 'P3c1', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z+1/2', 'x,x-y,z+1/2', '-x+y,y,z+1/2'], 'number': 158, 'point_group': '3m', 'schoenflies': 'C3v^3', 'short_h_m': 'P3c1', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z+1/2', 'x,x-y,z+1/2', '-x+y,y,z+1/2'], 'universal_h_m': 'P3c1'}, {'hall': ' P 3 -2c', 'hermann_mauguin': 'P31c', 'hermann_mauguin_u': 'P31c', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,z+1/2', '-x,-x+y,z+1/2', 'x-y,-y,z+1/2'], 'number': 159, 'point_group': '3m', 'schoenflies': 'C3v^4', 'short_h_m': 'P31c', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,z+1/2', '-x,-x+y,z+1/2', 'x-y,-y,z+1/2'], 'universal_h_m': 'P31c'}, {'hall': ' R 3 -2"', 'hermann_mauguin': 'R3m', 'hermann_mauguin_u': 'R3m', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'number': 160, 'point_group': '3m', 'schoenflies': 'C3v^5', 'short_h_m': 'R3m', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', '-y+2/3,-x+1/3,z+1/3', 'x+2/3,x-y+1/3,z+1/3', '-x+y+2/3,y+1/3,z+1/3', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', '-y+1/3,-x+2/3,z+2/3', 'x+1/3,x-y+2/3,z+2/3', '-x+y+1/3,y+2/3,z+2/3'], 'universal_h_m': 'R3m:H'}, {'hall': ' P 3* -2', 'hermann_mauguin': 'R3m', 'hermann_mauguin_u': 'R3m', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', 'y,x,z', 'z,y,x', 'x,z,y'], 'number': 160, 'point_group': '3m', 'schoenflies': 'C3v^5', 'short_h_m': 'R3m', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', 'y,x,z', 'z,y,x', 'x,z,y'], 'universal_h_m': 'R3m:R'}, {'hall': ' R 3 -2"c', 'hermann_mauguin': 'R3c', 'hermann_mauguin_u': 'R3c', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z+1/2', 'x,x-y,z+1/2', '-x+y,y,z+1/2'], 'number': 161, 'point_group': '3m', 'schoenflies': 'C3v^6', 'short_h_m': 'R3c', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,z+1/2', 'x,x-y,z+1/2', '-x+y,y,z+1/2', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', '-y+2/3,-x+1/3,z+5/6', 'x+2/3,x-y+1/3,z+5/6', '-x+y+2/3,y+1/3,z+5/6', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', '-y+1/3,-x+2/3,z+7/6', 'x+1/3,x-y+2/3,z+7/6', '-x+y+1/3,y+2/3,z+7/6'], 'universal_h_m': 'R3c:H'}, {'hall': ' P 3* -2n', 'hermann_mauguin': 'R3c', 'hermann_mauguin_u': 'R3c', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', 'y+1/2,x+1/2,z+1/2', 'z+1/2,y+1/2,x+1/2', 'x+1/2,z+1/2,y+1/2'], 'number': 161, 'point_group': '3m', 'schoenflies': 'C3v^6', 'short_h_m': 'R3c', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', 'y+1/2,x+1/2,z+1/2', 'z+1/2,y+1/2,x+1/2', 'x+1/2,z+1/2,y+1/2'], 'universal_h_m': 'R3c:R'}, {'hall': '-P 3 2', 'hermann_mauguin': 'P-31m', 'hermann_mauguin_u': 'P-31m', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z', 'x,x-y,-z', '-x+y,y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', 'y,x,z', '-x,-x+y,z', 'x-y,-y,z'], 'number': 162, 'point_group': '-3m', 'schoenflies': 'D3d^1', 'short_h_m': 'P-3m', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z', 'x,x-y,-z', '-x+y,y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', 'y,x,z', '-x,-x+y,z', 'x-y,-y,z'], 'universal_h_m': 'P-31m'}, {'hall': '-P 3 2c', 'hermann_mauguin': 'P-31c', 'hermann_mauguin_u': 'P-31c', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z+1/2', 'x,x-y,-z+1/2', '-x+y,y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', 'y,x,z-1/2', '-x,-x+y,z-1/2', 'x-y,-y,z-1/2'], 'number': 163, 'point_group': '-3m', 'schoenflies': 'D3d^2', 'short_h_m': 'P-3c', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', '-y,-x,-z+1/2', 'x,x-y,-z+1/2', '-x+y,y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', 'y,x,z-1/2', '-x,-x+y,z-1/2', 'x-y,-y,z-1/2'], 'universal_h_m': 'P-31c'}, {'hall': '-P 3 2"', 'hermann_mauguin': 'P-3m1', 'hermann_mauguin_u': 'P-3m1', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'number': 164, 'point_group': '-3m', 'schoenflies': 'D3d^3', 'short_h_m': 'P-3m', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'universal_h_m': 'P-3m1'}, {'hall': '-P 3 2"c', 'hermann_mauguin': 'P-3c1', 'hermann_mauguin_u': 'P-3c1', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z+1/2', '-x,-x+y,-z+1/2', 'x-y,-y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z-1/2', 'x,x-y,z-1/2', '-x+y,y,z-1/2'], 'number': 165, 'point_group': '-3m', 'schoenflies': 'D3d^4', 'short_h_m': 'P-3c', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z+1/2', '-x,-x+y,-z+1/2', 'x-y,-y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z-1/2', 'x,x-y,z-1/2', '-x+y,y,z-1/2'], 'universal_h_m': 'P-3c1'}, {'hall': '-R 3 2"', 'hermann_mauguin': 'R-3m', 'hermann_mauguin_u': 'R-3m', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z'], 'number': 166, 'point_group': '-3m', 'schoenflies': 'D3d^5', 'short_h_m': 'R-3m', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z', '-x,-x+y,-z', 'x-y,-y,-z', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z', 'x,x-y,z', '-x+y,y,z', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', 'y+2/3,x+1/3,-z+1/3', '-x+2/3,-x+y+1/3,-z+1/3', 'x-y+2/3,-y+1/3,-z+1/3', '-x+2/3,-y+1/3,-z+1/3', 'y+2/3,-x+y+1/3,-z+1/3', 'x-y+2/3,x+1/3,-z+1/3', '-y+2/3,-x+1/3,z+1/3', 'x+2/3,x-y+1/3,z+1/3', '-x+y+2/3,y+1/3,z+1/3', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', 'y+1/3,x+2/3,-z+2/3', '-x+1/3,-x+y+2/3,-z+2/3', 'x-y+1/3,-y+2/3,-z+2/3', '-x+1/3,-y+2/3,-z+2/3', 'y+1/3,-x+y+2/3,-z+2/3', 'x-y+1/3,x+2/3,-z+2/3', '-y+1/3,-x+2/3,z+2/3', 'x+1/3,x-y+2/3,z+2/3', '-x+y+1/3,y+2/3,z+2/3'], 'universal_h_m': 'R-3m:H'}, {'hall': '-P 3* 2', 'hermann_mauguin': 'R-3m', 'hermann_mauguin_u': 'R-3m', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', '-y,-x,-z', '-z,-y,-x', '-x,-z,-y', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x', 'y,x,z', 'z,y,x', 'x,z,y'], 'number': 166, 'point_group': '-3m', 'schoenflies': 'D3d^5', 'short_h_m': 'R-3m', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', '-y,-x,-z', '-z,-y,-x', '-x,-z,-y', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x', 'y,x,z', 'z,y,x', 'x,z,y'], 'universal_h_m': 'R-3m:R'}, {'hall': '-R 3 2"c', 'hermann_mauguin': 'R-3c', 'hermann_mauguin_u': 'R-3c', 'ncsym': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z+1/2', '-x,-x+y,-z+1/2', 'x-y,-y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z-1/2', 'x,x-y,z-1/2', '-x+y,y,z-1/2'], 'number': 167, 'point_group': '-3m', 'schoenflies': 'D3d^6', 'short_h_m': 'R-3c', 'symops': ['x,y,z', '-y,x-y,z', '-x+y,-x,z', 'y,x,-z+1/2', '-x,-x+y,-z+1/2', 'x-y,-y,-z+1/2', '-x,-y,-z', 'y,-x+y,-z', 'x-y,x,-z', '-y,-x,z-1/2', 'x,x-y,z-1/2', '-x+y,y,z-1/2', 'x+2/3,y+1/3,z+1/3', '-y+2/3,x-y+1/3,z+1/3', '-x+y+2/3,-x+1/3,z+1/3', 'y+2/3,x+1/3,-z+5/6', '-x+2/3,-x+y+1/3,-z+5/6', 'x-y+2/3,-y+1/3,-z+5/6', '-x+2/3,-y+1/3,-z+1/3', 'y+2/3,-x+y+1/3,-z+1/3', 'x-y+2/3,x+1/3,-z+1/3', '-y+2/3,-x+1/3,z-1/6', 'x+2/3,x-y+1/3,z-1/6', '-x+y+2/3,y+1/3,z-1/6', 'x+1/3,y+2/3,z+2/3', '-y+1/3,x-y+2/3,z+2/3', '-x+y+1/3,-x+2/3,z+2/3', 'y+1/3,x+2/3,-z+7/6', '-x+1/3,-x+y+2/3,-z+7/6', 'x-y+1/3,-y+2/3,-z+7/6', '-x+1/3,-y+2/3,-z+2/3', 'y+1/3,-x+y+2/3,-z+2/3', 'x-y+1/3,x+2/3,-z+2/3', '-y+1/3,-x+2/3,z+1/6', 'x+1/3,x-y+2/3,z+1/6', '-x+y+1/3,y+2/3,z+1/6'], 'universal_h_m': 'R-3c:H'}, {'hall': '-P 3* 2n', 'hermann_mauguin': 'R-3c', 'hermann_mauguin_u': 'R-3c', 'ncsym': ['x,y,z', 'z,x,y', 'y,z,x', '-y+1/2,-x+1/2,-z+1/2', '-z+1/2,-y+1/2,-x+1/2', '-x+1/2,-z+1/2,-y+1/2', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x', 'y-1/2,x-1/2,z-1/2', 'z-1/2,y-1/2,x-1/2', 'x-1/2,z-1/2,y-1/2'], 'number': 167, 'point_group': '-3m', 'schoenflies': 'D3d^6', 'short_h_m': 'R-3c', 'symops': ['x,y,z', 'z,x,y', 'y,z,x', '-y+1/2,-x+1/2,-z+1/2', '-z+1/2,-y+1/2,-x+1/2', '-x+1/2,-z+1/2,-y+1/2', '-x,-y,-z', '-z,-x,-y', '-y,-z,-x', 'y-1/2,x-1/2,z-1/2', 'z-1/2,y-1/2,x-1/2', 'x-1/2,z-1/2,y-1/2'], 'universal_h_m': 'R-3c:R'}, {'hall': ' P 6', 'hermann_mauguin': 'P6', 'hermann_mauguin_u': 'P6', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z'], 'number': 168, 'point_group': '6', 'schoenflies': 'C6^1', 'short_h_m': 'P6', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z'], 'universal_h_m': 'P6'}, {'hall': ' P 61', 'hermann_mauguin': 'P61', 'hermann_mauguin_u': 'P6_1', 'ncsym': ['x,y,z', 'x-y,x,z+1/6', '-y,x-y,z+1/3', '-x,-y,z+1/2', '-x+y,-x,z+2/3', 'y,-x+y,z+5/6'], 'number': 169, 'point_group': '6', 'schoenflies': 'C6^2', 'short_h_m': 'P6_1', 'symops': ['x,y,z', 'x-y,x,z+1/6', '-y,x-y,z+1/3', '-x,-y,z+1/2', '-x+y,-x,z+2/3', 'y,-x+y,z+5/6'], 'universal_h_m': 'P61'}, {'hall': ' P 65', 'hermann_mauguin': 'P65', 'hermann_mauguin_u': 'P6_5', 'ncsym': ['x,y,z', 'x-y,x,z+5/6', '-y,x-y,z+2/3', '-x,-y,z+1/2', '-x+y,-x,z+1/3', 'y,-x+y,z+1/6'], 'number': 170, 'point_group': '6', 'schoenflies': 'C6^3', 'short_h_m': 'P6_5', 'symops': ['x,y,z', 'x-y,x,z+5/6', '-y,x-y,z+2/3', '-x,-y,z+1/2', '-x+y,-x,z+1/3', 'y,-x+y,z+1/6'], 'universal_h_m': 'P65'}, {'hall': ' P 62', 'hermann_mauguin': 'P62', 'hermann_mauguin_u': 'P6_2', 'ncsym': ['x,y,z', 'x-y,x,z+1/3', '-y,x-y,z+2/3', '-x,-y,z', '-x+y,-x,z+1/3', 'y,-x+y,z+2/3'], 'number': 171, 'point_group': '6', 'schoenflies': 'C6^4', 'short_h_m': 'P6_2', 'symops': ['x,y,z', 'x-y,x,z+1/3', '-y,x-y,z+2/3', '-x,-y,z', '-x+y,-x,z+1/3', 'y,-x+y,z+2/3'], 'universal_h_m': 'P62'}, {'hall': ' P 64', 'hermann_mauguin': 'P64', 'hermann_mauguin_u': 'P6_4', 'ncsym': ['x,y,z', 'x-y,x,z+2/3', '-y,x-y,z+1/3', '-x,-y,z', '-x+y,-x,z+2/3', 'y,-x+y,z+1/3'], 'number': 172, 'point_group': '6', 'schoenflies': 'C6^5', 'short_h_m': 'P6_4', 'symops': ['x,y,z', 'x-y,x,z+2/3', '-y,x-y,z+1/3', '-x,-y,z', '-x+y,-x,z+2/3', 'y,-x+y,z+1/3'], 'universal_h_m': 'P64'}, {'hall': ' P 6c', 'hermann_mauguin': 'P63', 'hermann_mauguin_u': 'P6_3', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2'], 'number': 173, 'point_group': '6', 'schoenflies': 'C6^6', 'short_h_m': 'P6_3', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2'], 'universal_h_m': 'P63'}, {'hall': ' P -6', 'hermann_mauguin': 'P-6', 'hermann_mauguin_u': 'P-6', 'ncsym': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z'], 'number': 174, 'point_group': '-6', 'schoenflies': 'C3h^1', 'short_h_m': 'P-6', 'symops': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z'], 'universal_h_m': 'P-6'}, {'hall': '-P 6', 'hermann_mauguin': 'P6/m', 'hermann_mauguin_u': 'P6/m', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z'], 'number': 175, 'point_group': '6/m', 'schoenflies': 'C6h^1', 'short_h_m': 'P6/m', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z'], 'universal_h_m': 'P6/m'}, {'hall': '-P 6c', 'hermann_mauguin': 'P63/m', 'hermann_mauguin_u': 'P6_3/m', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2'], 'number': 176, 'point_group': '6/m', 'schoenflies': 'C6h^2', 'short_h_m': 'P6_3/m', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2'], 'universal_h_m': 'P63/m'}, {'hall': ' P 6 2', 'hermann_mauguin': 'P622', 'hermann_mauguin_u': 'P622', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z'], 'number': 177, 'point_group': '622', 'schoenflies': 'D6^1', 'short_h_m': 'P622', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z'], 'universal_h_m': 'P622'}, {'hall': ' P 61 2 (0 0 5)', 'hermann_mauguin': 'P6122', 'hermann_mauguin_u': 'P6_122', 'ncsym': ['x,y,z', 'x-y,x,z+1/6', '-y,x-y,z+1/3', '-x,-y,z+1/2', '-x+y,-x,z+2/3', 'y,-x+y,z+5/6', '-y,-x,-z+5/6', 'x-y,-y,-z', 'x,x-y,-z+1/6', 'y,x,-z+1/3', '-x+y,y,-z+1/2', '-x,-x+y,-z+2/3'], 'number': 178, 'point_group': '622', 'schoenflies': 'D6^2', 'short_h_m': 'P6_122', 'symops': ['x,y,z', 'x-y,x,z+1/6', '-y,x-y,z+1/3', '-x,-y,z+1/2', '-x+y,-x,z+2/3', 'y,-x+y,z+5/6', '-y,-x,-z+5/6', 'x-y,-y,-z', 'x,x-y,-z+1/6', 'y,x,-z+1/3', '-x+y,y,-z+1/2', '-x,-x+y,-z+2/3'], 'universal_h_m': 'P6122'}, {'hall': ' P 65 2 (0 0 1)', 'hermann_mauguin': 'P6522', 'hermann_mauguin_u': 'P6_522', 'ncsym': ['x,y,z', 'x-y,x,z+5/6', '-y,x-y,z+2/3', '-x,-y,z+1/2', '-x+y,-x,z+1/3', 'y,-x+y,z+1/6', '-y,-x,-z+1/6', 'x-y,-y,-z', 'x,x-y,-z+5/6', 'y,x,-z+2/3', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/3'], 'number': 179, 'point_group': '622', 'schoenflies': 'D6^3', 'short_h_m': 'P6_522', 'symops': ['x,y,z', 'x-y,x,z+5/6', '-y,x-y,z+2/3', '-x,-y,z+1/2', '-x+y,-x,z+1/3', 'y,-x+y,z+1/6', '-y,-x,-z+1/6', 'x-y,-y,-z', 'x,x-y,-z+5/6', 'y,x,-z+2/3', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/3'], 'universal_h_m': 'P6522'}, {'hall': ' P 62 2 (0 0 4)', 'hermann_mauguin': 'P6222', 'hermann_mauguin_u': 'P6_222', 'ncsym': ['x,y,z', 'x-y,x,z+1/3', '-y,x-y,z+2/3', '-x,-y,z', '-x+y,-x,z+1/3', 'y,-x+y,z+2/3', '-y,-x,-z+2/3', 'x-y,-y,-z', 'x,x-y,-z+1/3', 'y,x,-z+2/3', '-x+y,y,-z', '-x,-x+y,-z+1/3'], 'number': 180, 'point_group': '622', 'schoenflies': 'D6^4', 'short_h_m': 'P6_222', 'symops': ['x,y,z', 'x-y,x,z+1/3', '-y,x-y,z+2/3', '-x,-y,z', '-x+y,-x,z+1/3', 'y,-x+y,z+2/3', '-y,-x,-z+2/3', 'x-y,-y,-z', 'x,x-y,-z+1/3', 'y,x,-z+2/3', '-x+y,y,-z', '-x,-x+y,-z+1/3'], 'universal_h_m': 'P6222'}, {'hall': ' P 64 2 (0 0 2)', 'hermann_mauguin': 'P6422', 'hermann_mauguin_u': 'P6_422', 'ncsym': ['x,y,z', 'x-y,x,z+2/3', '-y,x-y,z+1/3', '-x,-y,z', '-x+y,-x,z+2/3', 'y,-x+y,z+1/3', '-y,-x,-z+1/3', 'x-y,-y,-z', 'x,x-y,-z+2/3', 'y,x,-z+1/3', '-x+y,y,-z', '-x,-x+y,-z+2/3'], 'number': 181, 'point_group': '622', 'schoenflies': 'D6^5', 'short_h_m': 'P6_422', 'symops': ['x,y,z', 'x-y,x,z+2/3', '-y,x-y,z+1/3', '-x,-y,z', '-x+y,-x,z+2/3', 'y,-x+y,z+1/3', '-y,-x,-z+1/3', 'x-y,-y,-z', 'x,x-y,-z+2/3', 'y,x,-z+1/3', '-x+y,y,-z', '-x,-x+y,-z+2/3'], 'universal_h_m': 'P6422'}, {'hall': ' P 6c 2c', 'hermann_mauguin': 'P6322', 'hermann_mauguin_u': 'P6_322', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z'], 'number': 182, 'point_group': '622', 'schoenflies': 'D6^6', 'short_h_m': 'P6_322', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z'], 'universal_h_m': 'P6322'}, {'hall': ' P 6 -2', 'hermann_mauguin': 'P6mm', 'hermann_mauguin_u': 'P6mm', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'number': 183, 'point_group': '6mm', 'schoenflies': 'C6v^1', 'short_h_m': 'P6mm', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'universal_h_m': 'P6mm'}, {'hall': ' P 6 -2c', 'hermann_mauguin': 'P6cc', 'hermann_mauguin_u': 'P6cc', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', 'y,x,z+1/2', '-x+y,y,z+1/2', '-x,-x+y,z+1/2', '-y,-x,z+1/2', 'x-y,-y,z+1/2', 'x,x-y,z+1/2'], 'number': 184, 'point_group': '6mm', 'schoenflies': 'C6v^2', 'short_h_m': 'P6cc', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', 'y,x,z+1/2', '-x+y,y,z+1/2', '-x,-x+y,z+1/2', '-y,-x,z+1/2', 'x-y,-y,z+1/2', 'x,x-y,z+1/2'], 'universal_h_m': 'P6cc'}, {'hall': ' P 6c -2', 'hermann_mauguin': 'P63cm', 'hermann_mauguin_u': 'P6_3cm', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', 'y,x,z', '-x+y,y,z+1/2', '-x,-x+y,z', '-y,-x,z+1/2', 'x-y,-y,z', 'x,x-y,z+1/2'], 'number': 185, 'point_group': '6mm', 'schoenflies': 'C6v^3', 'short_h_m': 'P6_3cm', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', 'y,x,z', '-x+y,y,z+1/2', '-x,-x+y,z', '-y,-x,z+1/2', 'x-y,-y,z', 'x,x-y,z+1/2'], 'universal_h_m': 'P63cm'}, {'hall': ' P 6c -2c', 'hermann_mauguin': 'P63mc', 'hermann_mauguin_u': 'P6_3mc', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', 'y,x,z+1/2', '-x+y,y,z', '-x,-x+y,z+1/2', '-y,-x,z', 'x-y,-y,z+1/2', 'x,x-y,z'], 'number': 186, 'point_group': '6mm', 'schoenflies': 'C6v^4', 'short_h_m': 'P6_3mc', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', 'y,x,z+1/2', '-x+y,y,z', '-x,-x+y,z+1/2', '-y,-x,z', 'x-y,-y,z+1/2', 'x,x-y,z'], 'universal_h_m': 'P63mc'}, {'hall': ' P -6 2', 'hermann_mauguin': 'P-6m2', 'hermann_mauguin_u': 'P-6m2', 'ncsym': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z', '-y,-x,-z', '-x+y,y,z', 'x,x-y,-z', '-y,-x,z', '-x+y,y,-z', 'x,x-y,z'], 'number': 187, 'point_group': '-6m2', 'schoenflies': 'D3h^1', 'short_h_m': 'P-6m2', 'symops': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z', '-y,-x,-z', '-x+y,y,z', 'x,x-y,-z', '-y,-x,z', '-x+y,y,-z', 'x,x-y,z'], 'universal_h_m': 'P-6m2'}, {'hall': ' P -6c 2', 'hermann_mauguin': 'P-6c2', 'hermann_mauguin_u': 'P-6c2', 'ncsym': ['x,y,z', '-x+y,-x,-z+1/2', '-y,x-y,z', 'x,y,-z+1/2', '-x+y,-x,z', '-y,x-y,-z+1/2', '-y,-x,-z', '-x+y,y,z+1/2', 'x,x-y,-z', '-y,-x,z+1/2', '-x+y,y,-z', 'x,x-y,z+1/2'], 'number': 188, 'point_group': '-6m2', 'schoenflies': 'D3h^2', 'short_h_m': 'P-6c2', 'symops': ['x,y,z', '-x+y,-x,-z+1/2', '-y,x-y,z', 'x,y,-z+1/2', '-x+y,-x,z', '-y,x-y,-z+1/2', '-y,-x,-z', '-x+y,y,z+1/2', 'x,x-y,-z', '-y,-x,z+1/2', '-x+y,y,-z', 'x,x-y,z+1/2'], 'universal_h_m': 'P-6c2'}, {'hall': ' P -6 -2', 'hermann_mauguin': 'P-62m', 'hermann_mauguin_u': 'P-62m', 'ncsym': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z', 'y,x,z', 'x-y,-y,-z', '-x,-x+y,z', 'y,x,-z', 'x-y,-y,z', '-x,-x+y,-z'], 'number': 189, 'point_group': '-6m2', 'schoenflies': 'D3h^3', 'short_h_m': 'P-62m', 'symops': ['x,y,z', '-x+y,-x,-z', '-y,x-y,z', 'x,y,-z', '-x+y,-x,z', '-y,x-y,-z', 'y,x,z', 'x-y,-y,-z', '-x,-x+y,z', 'y,x,-z', 'x-y,-y,z', '-x,-x+y,-z'], 'universal_h_m': 'P-62m'}, {'hall': ' P -6c -2c', 'hermann_mauguin': 'P-62c', 'hermann_mauguin_u': 'P-62c', 'ncsym': ['x,y,z', '-x+y,-x,-z+1/2', '-y,x-y,z', 'x,y,-z+1/2', '-x+y,-x,z', '-y,x-y,-z+1/2', 'y,x,z+1/2', 'x-y,-y,-z', '-x,-x+y,z+1/2', 'y,x,-z', 'x-y,-y,z+1/2', '-x,-x+y,-z'], 'number': 190, 'point_group': '-6m2', 'schoenflies': 'D3h^4', 'short_h_m': 'P-62c', 'symops': ['x,y,z', '-x+y,-x,-z+1/2', '-y,x-y,z', 'x,y,-z+1/2', '-x+y,-x,z', '-y,x-y,-z+1/2', 'y,x,z+1/2', 'x-y,-y,-z', '-x,-x+y,z+1/2', 'y,x,-z', 'x-y,-y,z+1/2', '-x,-x+y,-z'], 'universal_h_m': 'P-62c'}, {'hall': '-P 6 2', 'hermann_mauguin': 'P6/mmm', 'hermann_mauguin_u': 'P6/mmm', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'number': 191, 'point_group': '6/mmm', 'schoenflies': 'D6h^1', 'short_h_m': 'P6/mmm', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'universal_h_m': 'P6/mmm'}, {'hall': '-P 6 2c', 'hermann_mauguin': 'P6/mcc', 'hermann_mauguin_u': 'P6/mcc', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z+1/2', 'x-y,-y,-z+1/2', 'x,x-y,-z+1/2', 'y,x,-z+1/2', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z-1/2', '-x+y,y,z-1/2', '-x,-x+y,z-1/2', '-y,-x,z-1/2', 'x-y,-y,z-1/2', 'x,x-y,z-1/2'], 'number': 192, 'point_group': '6/mmm', 'schoenflies': 'D6h^2', 'short_h_m': 'P6/mcc', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z+1/2', 'x-y,-y,-z+1/2', 'x,x-y,-z+1/2', 'y,x,-z+1/2', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z-1/2', '-x+y,y,z-1/2', '-x,-x+y,z-1/2', '-y,-x,z-1/2', 'x-y,-y,z-1/2', 'x,x-y,z-1/2'], 'universal_h_m': 'P6/mcc'}, {'hall': '-P 6c 2', 'hermann_mauguin': 'P63/mcm', 'hermann_mauguin_u': 'P6_3/mcm', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z', 'x-y,-y,-z+1/2', 'x,x-y,-z', 'y,x,-z+1/2', '-x+y,y,-z', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2', 'y,x,z', '-x+y,y,z-1/2', '-x,-x+y,z', '-y,-x,z-1/2', 'x-y,-y,z', 'x,x-y,z-1/2'], 'number': 193, 'point_group': '6/mmm', 'schoenflies': 'D6h^3', 'short_h_m': 'P6_3/mcm', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z', 'x-y,-y,-z+1/2', 'x,x-y,-z', 'y,x,-z+1/2', '-x+y,y,-z', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2', 'y,x,z', '-x+y,y,z-1/2', '-x,-x+y,z', '-y,-x,z-1/2', 'x-y,-y,z', 'x,x-y,z-1/2'], 'universal_h_m': 'P63/mcm'}, {'hall': '-P 6c 2c', 'hermann_mauguin': 'P63/mmc', 'hermann_mauguin_u': 'P6_3/mmc', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2', 'y,x,z-1/2', '-x+y,y,z', '-x,-x+y,z-1/2', '-y,-x,z', 'x-y,-y,z-1/2', 'x,x-y,z'], 'number': 194, 'point_group': '6/mmm', 'schoenflies': 'D6h^4', 'short_h_m': 'P6_3/mmc', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z-1/2', 'y,-x+y,-z', 'x,y,-z-1/2', 'x-y,x,-z', '-y,x-y,-z-1/2', 'y,x,z-1/2', '-x+y,y,z', '-x,-x+y,z-1/2', '-y,-x,z', 'x-y,-y,z-1/2', 'x,x-y,z'], 'universal_h_m': 'P63/mmc'}, {'hall': ' P 2 2 3', 'hermann_mauguin': 'P23', 'hermann_mauguin_u': 'P23', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x'], 'number': 195, 'point_group': '23', 'schoenflies': 'T^1', 'short_h_m': 'P23', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x'], 'universal_h_m': 'P23'}, {'hall': ' F 2 2 3', 'hermann_mauguin': 'F23', 'hermann_mauguin_u': 'F23', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x'], 'number': 196, 'point_group': '23', 'schoenflies': 'T^2', 'short_h_m': 'F23', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'z,-x+1/2,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-y,-z+1/2,x+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', 'z+1/2,x,y+1/2', '-z+1/2,-x,y+1/2', 'z+1/2,-x,-y+1/2', '-z+1/2,x,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z,x+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', 'z+1/2,x+1/2,y', '-z+1/2,-x+1/2,y', 'z+1/2,-x+1/2,-y', '-z+1/2,x+1/2,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', '-y+1/2,z+1/2,-x', '-y+1/2,-z+1/2,x'], 'universal_h_m': 'F23'}, {'hall': ' I 2 2 3', 'hermann_mauguin': 'I23', 'hermann_mauguin_u': 'I23', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x'], 'number': 197, 'point_group': '23', 'schoenflies': 'T^3', 'short_h_m': 'I23', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', 'z+1/2,x+1/2,y+1/2', '-z+1/2,-x+1/2,y+1/2', 'z+1/2,-x+1/2,-y+1/2', '-z+1/2,x+1/2,-y+1/2', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,-x+1/2', '-y+1/2,-z+1/2,x+1/2'], 'universal_h_m': 'I23'}, {'hall': ' P 2ac 2ab 3', 'hermann_mauguin': 'P213', 'hermann_mauguin_u': 'P2_13', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', 'z,x,y', '-z+1/2,-x,y+1/2', 'z+1/2,-x+1/2,-y', '-z,x+1/2,-y+1/2', 'y,z,x', 'y+1/2,-z+1/2,-x', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2'], 'number': 198, 'point_group': '23', 'schoenflies': 'T^4', 'short_h_m': 'P2_13', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', 'z,x,y', '-z+1/2,-x,y+1/2', 'z+1/2,-x+1/2,-y', '-z,x+1/2,-y+1/2', 'y,z,x', 'y+1/2,-z+1/2,-x', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2'], 'universal_h_m': 'P213'}, {'hall': ' I 2b 2c 3', 'hermann_mauguin': 'I213', 'hermann_mauguin_u': 'I2_13', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x,y', '-z,-x+1/2,y', 'z,-x,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z,x', 'y,-z,-x+1/2', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2'], 'number': 199, 'point_group': '23', 'schoenflies': 'T^5', 'short_h_m': 'I2_13', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x,y', '-z,-x+1/2,y', 'z,-x,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z,x', 'y,-z,-x+1/2', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1,-z+1', 'z+1/2,x+1/2,y+1/2', '-z+1/2,-x+1,y+1/2', 'z+1/2,-x+1/2,-y+1', '-z+1/2,x+1,-y+1', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1', '-y+1/2,z+1,-x+1', '-y+1,-z+1/2,x+1'], 'universal_h_m': 'I213'}, {'hall': '-P 2 2 3', 'hermann_mauguin': 'Pm-3', 'hermann_mauguin_u': 'Pm-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x'], 'number': 200, 'point_group': 'm-3', 'schoenflies': 'Th^1', 'short_h_m': 'Pm-3', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x'], 'universal_h_m': 'Pm-3'}, {'hall': ' P 2 2 3 -1n', 'hermann_mauguin': 'Pn-3', 'hermann_mauguin_u': 'Pn-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2'], 'number': 201, 'point_group': 'm-3', 'schoenflies': 'Th^2', 'short_h_m': 'Pn-3', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2'], 'universal_h_m': 'Pn-3:1'}, {'hall': '-P 2ab 2bc 3', 'hermann_mauguin': 'Pn-3', 'hermann_mauguin_u': 'Pn-3', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', 'z,x,y', '-z+1/2,-x+1/2,y', 'z,-x+1/2,-y+1/2', '-z+1/2,x,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z+1/2,x', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y,z-1/2', '-z,-x,-y', 'z-1/2,x-1/2,-y', '-z,x-1/2,y-1/2', 'z-1/2,-x,y-1/2', '-y,-z,-x', '-y,z-1/2,x-1/2', 'y-1/2,-z,x-1/2', 'y-1/2,z-1/2,-x'], 'number': 201, 'point_group': 'm-3', 'schoenflies': 'Th^2', 'short_h_m': 'Pn-3', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', 'z,x,y', '-z+1/2,-x+1/2,y', 'z,-x+1/2,-y+1/2', '-z+1/2,x,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z+1/2,x', '-x,-y,-z', 'x-1/2,y-1/2,-z', '-x,y-1/2,z-1/2', 'x-1/2,-y,z-1/2', '-z,-x,-y', 'z-1/2,x-1/2,-y', '-z,x-1/2,y-1/2', 'z-1/2,-x,y-1/2', '-y,-z,-x', '-y,z-1/2,x-1/2', 'y-1/2,-z,x-1/2', 'y-1/2,z-1/2,-x'], 'universal_h_m': 'Pn-3:2'}, {'hall': '-F 2 2 3', 'hermann_mauguin': 'Fm-3', 'hermann_mauguin_u': 'Fm-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x'], 'number': 202, 'point_group': 'm-3', 'schoenflies': 'Th^3', 'short_h_m': 'Fm-3', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'z,-x+1/2,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-y,-z+1/2,x+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', '-z,-x+1/2,-y+1/2', 'z,x+1/2,-y+1/2', '-z,x+1/2,y+1/2', 'z,-x+1/2,y+1/2', '-y,-z+1/2,-x+1/2', '-y,z+1/2,x+1/2', 'y,-z+1/2,x+1/2', 'y,z+1/2,-x+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', 'z+1/2,x,y+1/2', '-z+1/2,-x,y+1/2', 'z+1/2,-x,-y+1/2', '-z+1/2,x,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z,x+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2', '-z+1/2,-x,-y+1/2', 'z+1/2,x,-y+1/2', '-z+1/2,x,y+1/2', 'z+1/2,-x,y+1/2', '-y+1/2,-z,-x+1/2', '-y+1/2,z,x+1/2', 'y+1/2,-z,x+1/2', 'y+1/2,z,-x+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', 'z+1/2,x+1/2,y', '-z+1/2,-x+1/2,y', 'z+1/2,-x+1/2,-y', '-z+1/2,x+1/2,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', '-y+1/2,z+1/2,-x', '-y+1/2,-z+1/2,x', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', '-z+1/2,-x+1/2,-y', 'z+1/2,x+1/2,-y', '-z+1/2,x+1/2,y', 'z+1/2,-x+1/2,y', '-y+1/2,-z+1/2,-x', '-y+1/2,z+1/2,x', 'y+1/2,-z+1/2,x', 'y+1/2,z+1/2,-x'], 'universal_h_m': 'Fm-3'}, {'hall': ' F 2 2 3 -1d', 'hermann_mauguin': 'Fd-3', 'hermann_mauguin_u': 'Fd-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x+1/4,-y+1/4,-z+1/4', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', 'x+1/4,-y+1/4,z+1/4', '-z+1/4,-x+1/4,-y+1/4', 'z+1/4,x+1/4,-y+1/4', '-z+1/4,x+1/4,y+1/4', 'z+1/4,-x+1/4,y+1/4', '-y+1/4,-z+1/4,-x+1/4', '-y+1/4,z+1/4,x+1/4', 'y+1/4,-z+1/4,x+1/4', 'y+1/4,z+1/4,-x+1/4'], 'number': 203, 'point_group': 'm-3', 'schoenflies': 'Th^4', 'short_h_m': 'Fd-3', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x+1/4,-y+1/4,-z+1/4', 'x+1/4,y+1/4,-z+1/4', '-x+1/4,y+1/4,z+1/4', 'x+1/4,-y+1/4,z+1/4', '-z+1/4,-x+1/4,-y+1/4', 'z+1/4,x+1/4,-y+1/4', '-z+1/4,x+1/4,y+1/4', 'z+1/4,-x+1/4,y+1/4', '-y+1/4,-z+1/4,-x+1/4', '-y+1/4,z+1/4,x+1/4', 'y+1/4,-z+1/4,x+1/4', 'y+1/4,z+1/4,-x+1/4', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'z,-x+1/2,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-y,-z+1/2,x+1/2', '-x+1/4,-y+3/4,-z+3/4', 'x+1/4,y+3/4,-z+3/4', '-x+1/4,y+3/4,z+3/4', 'x+1/4,-y+3/4,z+3/4', '-z+1/4,-x+3/4,-y+3/4', 'z+1/4,x+3/4,-y+3/4', '-z+1/4,x+3/4,y+3/4', 'z+1/4,-x+3/4,y+3/4', '-y+1/4,-z+3/4,-x+3/4', '-y+1/4,z+3/4,x+3/4', 'y+1/4,-z+3/4,x+3/4', 'y+1/4,z+3/4,-x+3/4', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', 'z+1/2,x,y+1/2', '-z+1/2,-x,y+1/2', 'z+1/2,-x,-y+1/2', '-z+1/2,x,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z,x+1/2', '-x+3/4,-y+1/4,-z+3/4', 'x+3/4,y+1/4,-z+3/4', '-x+3/4,y+1/4,z+3/4', 'x+3/4,-y+1/4,z+3/4', '-z+3/4,-x+1/4,-y+3/4', 'z+3/4,x+1/4,-y+3/4', '-z+3/4,x+1/4,y+3/4', 'z+3/4,-x+1/4,y+3/4', '-y+3/4,-z+1/4,-x+3/4', '-y+3/4,z+1/4,x+3/4', 'y+3/4,-z+1/4,x+3/4', 'y+3/4,z+1/4,-x+3/4', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', 'z+1/2,x+1/2,y', '-z+1/2,-x+1/2,y', 'z+1/2,-x+1/2,-y', '-z+1/2,x+1/2,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', '-y+1/2,z+1/2,-x', '-y+1/2,-z+1/2,x', '-x+3/4,-y+3/4,-z+1/4', 'x+3/4,y+3/4,-z+1/4', '-x+3/4,y+3/4,z+1/4', 'x+3/4,-y+3/4,z+1/4', '-z+3/4,-x+3/4,-y+1/4', 'z+3/4,x+3/4,-y+1/4', '-z+3/4,x+3/4,y+1/4', 'z+3/4,-x+3/4,y+1/4', '-y+3/4,-z+3/4,-x+1/4', '-y+3/4,z+3/4,x+1/4', 'y+3/4,-z+3/4,x+1/4', 'y+3/4,z+3/4,-x+1/4'], 'universal_h_m': 'Fd-3:1'}, {'hall': '-F 2uv 2vw 3', 'hermann_mauguin': 'Fd-3', 'hermann_mauguin_u': 'Fd-3', 'ncsym': ['x,y,z', '-x+1/4,-y+1/4,z', 'x,-y+1/4,-z+1/4', '-x+1/4,y,-z+1/4', 'z,x,y', '-z+1/4,-x+1/4,y', 'z,-x+1/4,-y+1/4', '-z+1/4,x,-y+1/4', 'y,z,x', 'y,-z+1/4,-x+1/4', '-y+1/4,z,-x+1/4', '-y+1/4,-z+1/4,x', '-x,-y,-z', 'x-1/4,y-1/4,-z', '-x,y-1/4,z-1/4', 'x-1/4,-y,z-1/4', '-z,-x,-y', 'z-1/4,x-1/4,-y', '-z,x-1/4,y-1/4', 'z-1/4,-x,y-1/4', '-y,-z,-x', '-y,z-1/4,x-1/4', 'y-1/4,-z,x-1/4', 'y-1/4,z-1/4,-x'], 'number': 203, 'point_group': 'm-3', 'schoenflies': 'Th^4', 'short_h_m': 'Fd-3', 'symops': ['x,y,z', '-x+1/4,-y+1/4,z', 'x,-y+1/4,-z+1/4', '-x+1/4,y,-z+1/4', 'z,x,y', '-z+1/4,-x+1/4,y', 'z,-x+1/4,-y+1/4', '-z+1/4,x,-y+1/4', 'y,z,x', 'y,-z+1/4,-x+1/4', '-y+1/4,z,-x+1/4', '-y+1/4,-z+1/4,x', '-x,-y,-z', 'x-1/4,y-1/4,-z', '-x,y-1/4,z-1/4', 'x-1/4,-y,z-1/4', '-z,-x,-y', 'z-1/4,x-1/4,-y', '-z,x-1/4,y-1/4', 'z-1/4,-x,y-1/4', '-y,-z,-x', '-y,z-1/4,x-1/4', 'y-1/4,-z,x-1/4', 'y-1/4,z-1/4,-x', 'x,y+1/2,z+1/2', '-x+1/4,-y+3/4,z+1/2', 'x,-y+3/4,-z+3/4', '-x+1/4,y+1/2,-z+3/4', 'z,x+1/2,y+1/2', '-z+1/4,-x+3/4,y+1/2', 'z,-x+3/4,-y+3/4', '-z+1/4,x+1/2,-y+3/4', 'y,z+1/2,x+1/2', 'y,-z+3/4,-x+3/4', '-y+1/4,z+1/2,-x+3/4', '-y+1/4,-z+3/4,x+1/2', '-x,-y+1/2,-z+1/2', 'x-1/4,y+1/4,-z+1/2', '-x,y+1/4,z+1/4', 'x-1/4,-y+1/2,z+1/4', '-z,-x+1/2,-y+1/2', 'z-1/4,x+1/4,-y+1/2', '-z,x+1/4,y+1/4', 'z-1/4,-x+1/2,y+1/4', '-y,-z+1/2,-x+1/2', '-y,z+1/4,x+1/4', 'y-1/4,-z+1/2,x+1/4', 'y-1/4,z+1/4,-x+1/2', 'x+1/2,y,z+1/2', '-x+3/4,-y+1/4,z+1/2', 'x+1/2,-y+1/4,-z+3/4', '-x+3/4,y,-z+3/4', 'z+1/2,x,y+1/2', '-z+3/4,-x+1/4,y+1/2', 'z+1/2,-x+1/4,-y+3/4', '-z+3/4,x,-y+3/4', 'y+1/2,z,x+1/2', 'y+1/2,-z+1/4,-x+3/4', '-y+3/4,z,-x+3/4', '-y+3/4,-z+1/4,x+1/2', '-x+1/2,-y,-z+1/2', 'x+1/4,y-1/4,-z+1/2', '-x+1/2,y-1/4,z+1/4', 'x+1/4,-y,z+1/4', '-z+1/2,-x,-y+1/2', 'z+1/4,x-1/4,-y+1/2', '-z+1/2,x-1/4,y+1/4', 'z+1/4,-x,y+1/4', '-y+1/2,-z,-x+1/2', '-y+1/2,z-1/4,x+1/4', 'y+1/4,-z,x+1/4', 'y+1/4,z-1/4,-x+1/2', 'x+1/2,y+1/2,z', '-x+3/4,-y+3/4,z', 'x+1/2,-y+3/4,-z+1/4', '-x+3/4,y+1/2,-z+1/4', 'z+1/2,x+1/2,y', '-z+3/4,-x+3/4,y', 'z+1/2,-x+3/4,-y+1/4', '-z+3/4,x+1/2,-y+1/4', 'y+1/2,z+1/2,x', 'y+1/2,-z+3/4,-x+1/4', '-y+3/4,z+1/2,-x+1/4', '-y+3/4,-z+3/4,x', '-x+1/2,-y+1/2,-z', 'x+1/4,y+1/4,-z', '-x+1/2,y+1/4,z-1/4', 'x+1/4,-y+1/2,z-1/4', '-z+1/2,-x+1/2,-y', 'z+1/4,x+1/4,-y', '-z+1/2,x+1/4,y-1/4', 'z+1/4,-x+1/2,y-1/4', '-y+1/2,-z+1/2,-x', '-y+1/2,z+1/4,x-1/4', 'y+1/4,-z+1/2,x-1/4', 'y+1/4,z+1/4,-x'], 'universal_h_m': 'Fd-3:2'}, {'hall': '-I 2 2 3', 'hermann_mauguin': 'Im-3', 'hermann_mauguin_u': 'Im-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x'], 'number': 204, 'point_group': 'm-3', 'schoenflies': 'Th^5', 'short_h_m': 'Im-3', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x,-y,-z', 'x,y,-z', '-x,y,z', 'x,-y,z', '-z,-x,-y', 'z,x,-y', '-z,x,y', 'z,-x,y', '-y,-z,-x', '-y,z,x', 'y,-z,x', 'y,z,-x', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', 'z+1/2,x+1/2,y+1/2', '-z+1/2,-x+1/2,y+1/2', 'z+1/2,-x+1/2,-y+1/2', '-z+1/2,x+1/2,-y+1/2', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,-x+1/2', '-y+1/2,-z+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2'], 'universal_h_m': 'Im-3'}, {'hall': '-P 2ac 2ab 3', 'hermann_mauguin': 'Pa-3', 'hermann_mauguin_u': 'Pa-3', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', 'z,x,y', '-z+1/2,-x,y+1/2', 'z+1/2,-x+1/2,-y', '-z,x+1/2,-y+1/2', 'y,z,x', 'y+1/2,-z+1/2,-x', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y-1/2,z-1/2', '-z,-x,-y', 'z-1/2,x,-y-1/2', '-z-1/2,x-1/2,y', 'z,-x-1/2,y-1/2', '-y,-z,-x', '-y-1/2,z-1/2,x', 'y,-z-1/2,x-1/2', 'y-1/2,z,-x-1/2'], 'number': 205, 'point_group': 'm-3', 'schoenflies': 'Th^6', 'short_h_m': 'Pa-3', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z+1/2', 'z,x,y', '-z+1/2,-x,y+1/2', 'z+1/2,-x+1/2,-y', '-z,x+1/2,-y+1/2', 'y,z,x', 'y+1/2,-z+1/2,-x', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2', '-x,-y,-z', 'x-1/2,y,-z-1/2', '-x-1/2,y-1/2,z', 'x,-y-1/2,z-1/2', '-z,-x,-y', 'z-1/2,x,-y-1/2', '-z-1/2,x-1/2,y', 'z,-x-1/2,y-1/2', '-y,-z,-x', '-y-1/2,z-1/2,x', 'y,-z-1/2,x-1/2', 'y-1/2,z,-x-1/2'], 'universal_h_m': 'Pa-3'}, {'hall': '-I 2b 2c 3', 'hermann_mauguin': 'Ia-3', 'hermann_mauguin_u': 'Ia-3', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x,y', '-z,-x+1/2,y', 'z,-x,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z,x', 'y,-z,-x+1/2', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2', '-z,-x,-y', 'z,x-1/2,-y', '-z,x,y-1/2', 'z,-x-1/2,y-1/2', '-y,-z,-x', '-y,z,x-1/2', 'y,-z-1/2,x-1/2', 'y-1/2,z,-x-1/2'], 'number': 206, 'point_group': 'm-3', 'schoenflies': 'Th^7', 'short_h_m': 'Ia-3', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'z,x,y', '-z,-x+1/2,y', 'z,-x,-y+1/2', '-z,x+1/2,-y+1/2', 'y,z,x', 'y,-z,-x+1/2', '-y,z+1/2,-x+1/2', '-y+1/2,-z,x+1/2', '-x,-y,-z', 'x,y-1/2,-z', '-x,y,z-1/2', 'x,-y-1/2,z-1/2', '-z,-x,-y', 'z,x-1/2,-y', '-z,x,y-1/2', 'z,-x-1/2,y-1/2', '-y,-z,-x', '-y,z,x-1/2', 'y,-z-1/2,x-1/2', 'y-1/2,z,-x-1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'x+1/2,-y+1/2,-z+1', '-x+1/2,y+1,-z+1', 'z+1/2,x+1/2,y+1/2', '-z+1/2,-x+1,y+1/2', 'z+1/2,-x+1/2,-y+1', '-z+1/2,x+1,-y+1', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1', '-y+1/2,z+1,-x+1', '-y+1,-z+1/2,x+1', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y,z', '-z+1/2,-x+1/2,-y+1/2', 'z+1/2,x,-y+1/2', '-z+1/2,x+1/2,y', 'z+1/2,-x,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x', 'y+1/2,-z,x', 'y,z+1/2,-x'], 'universal_h_m': 'Ia-3'}, {'hall': ' P 4 2 3', 'hermann_mauguin': 'P432', 'hermann_mauguin_u': 'P432', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x'], 'number': 207, 'point_group': '432', 'schoenflies': 'O^1', 'short_h_m': 'P432', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x'], 'universal_h_m': 'P432'}, {'hall': ' P 4n 2 3', 'hermann_mauguin': 'P4232', 'hermann_mauguin_u': 'P4_232', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2'], 'number': 208, 'point_group': '432', 'schoenflies': 'O^2', 'short_h_m': 'P4_232', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2'], 'universal_h_m': 'P4232'}, {'hall': ' F 4 2 3', 'hermann_mauguin': 'F432', 'hermann_mauguin_u': 'F432', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x'], 'number': 209, 'point_group': '432', 'schoenflies': 'O^3', 'short_h_m': 'F432', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x+1/2,-z+1/2', 'z,x+1/2,y+1/2', '-x,z+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'x,-z+1/2,y+1/2', 'z,-x+1/2,-y+1/2', 'x,z+1/2,-y+1/2', '-z,x+1/2,-y+1/2', '-x,-z+1/2,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', 'z,y+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-z,-y+1/2,-x+1/2', '-y,-z+1/2,x+1/2', 'z,-y+1/2,x+1/2', '-z,y+1/2,x+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x,-z+1/2', 'z+1/2,x,y+1/2', '-x+1/2,z,y+1/2', '-z+1/2,-x,y+1/2', 'x+1/2,-z,y+1/2', 'z+1/2,-x,-y+1/2', 'x+1/2,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', 'z+1/2,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y,-x+1/2', '-y+1/2,-z,x+1/2', 'z+1/2,-y,x+1/2', '-z+1/2,y,x+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z', 'z+1/2,x+1/2,y', '-x+1/2,z+1/2,y', '-z+1/2,-x+1/2,y', 'x+1/2,-z+1/2,y', 'z+1/2,-x+1/2,-y', 'x+1/2,z+1/2,-y', '-z+1/2,x+1/2,-y', '-x+1/2,-z+1/2,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', 'z+1/2,y+1/2,-x', '-y+1/2,z+1/2,-x', '-z+1/2,-y+1/2,-x', '-y+1/2,-z+1/2,x', 'z+1/2,-y+1/2,x', '-z+1/2,y+1/2,x'], 'universal_h_m': 'F432'}, {'hall': ' F 4d 2 3', 'hermann_mauguin': 'F4132', 'hermann_mauguin_u': 'F4_132', 'ncsym': ['x,y,z', '-y+1/4,x+1/4,z+1/4', '-x,-y+1/2,z+1/2', 'y+3/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+1/4,-z+3/4', 'z,x,y', '-x+1/4,z+1/4,y+1/4', '-z,-x+1/2,y+1/2', 'x+3/4,-z+1/4,y+3/4', 'z,-x,-y', 'x+1/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+1/4,-y+3/4', 'y,z,x', 'y+1/2,-z,-x+1/2', 'z+1/4,y+3/4,-x+3/4', '-y+1/2,z+1/2,-x', '-z+1/4,-y+1/4,-x+1/4', '-y,-z,x', 'z+1/4,-y+3/4,x+3/4', '-z+3/4,y+3/4,x+1/4'], 'number': 210, 'point_group': '432', 'schoenflies': 'O^4', 'short_h_m': 'F4_132', 'symops': ['x,y,z', '-y+1/4,x+1/4,z+1/4', '-x,-y+1/2,z+1/2', 'y+3/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+1/4,-z+3/4', 'z,x,y', '-x+1/4,z+1/4,y+1/4', '-z,-x+1/2,y+1/2', 'x+3/4,-z+1/4,y+3/4', 'z,-x,-y', 'x+1/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+1/4,-y+3/4', 'y,z,x', 'y+1/2,-z,-x+1/2', 'z+1/4,y+3/4,-x+3/4', '-y+1/2,z+1/2,-x', '-z+1/4,-y+1/4,-x+1/4', '-y,-z,x', 'z+1/4,-y+3/4,x+3/4', '-z+3/4,y+3/4,x+1/4', 'x,y+1/2,z+1/2', '-y+1/4,x+3/4,z+3/4', '-x,-y+1,z+1', 'y+3/4,-x+3/4,z+5/4', 'x,-y+1/2,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x,y+1,-z+1', '-y+3/4,-x+3/4,-z+5/4', 'z,x+1/2,y+1/2', '-x+1/4,z+3/4,y+3/4', '-z,-x+1,y+1', 'x+3/4,-z+3/4,y+5/4', 'z,-x+1/2,-y+1/2', 'x+1/4,z+3/4,-y+3/4', '-z,x+1,-y+1', '-x+3/4,-z+3/4,-y+5/4', 'y,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1', 'z+1/4,y+5/4,-x+5/4', '-y+1/2,z+1,-x+1/2', '-z+1/4,-y+3/4,-x+3/4', '-y,-z+1/2,x+1/2', 'z+1/4,-y+5/4,x+5/4', '-z+3/4,y+5/4,x+3/4', 'x+1/2,y,z+1/2', '-y+3/4,x+1/4,z+3/4', '-x+1/2,-y+1/2,z+1', 'y+5/4,-x+1/4,z+5/4', 'x+1/2,-y,-z+1/2', 'y+3/4,x+1/4,-z+3/4', '-x+1/2,y+1/2,-z+1', '-y+5/4,-x+1/4,-z+5/4', 'z+1/2,x,y+1/2', '-x+3/4,z+1/4,y+3/4', '-z+1/2,-x+1/2,y+1', 'x+5/4,-z+1/4,y+5/4', 'z+1/2,-x,-y+1/2', 'x+3/4,z+1/4,-y+3/4', '-z+1/2,x+1/2,-y+1', '-x+5/4,-z+1/4,-y+5/4', 'y+1/2,z,x+1/2', 'y+1,-z,-x+1', 'z+3/4,y+3/4,-x+5/4', '-y+1,z+1/2,-x+1/2', '-z+3/4,-y+1/4,-x+3/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+5/4', '-z+5/4,y+3/4,x+3/4', 'x+1/2,y+1/2,z', '-y+3/4,x+3/4,z+1/4', '-x+1/2,-y+1,z+1/2', 'y+5/4,-x+3/4,z+3/4', 'x+1/2,-y+1/2,-z', 'y+3/4,x+3/4,-z+1/4', '-x+1/2,y+1,-z+1/2', '-y+5/4,-x+3/4,-z+3/4', 'z+1/2,x+1/2,y', '-x+3/4,z+3/4,y+1/4', '-z+1/2,-x+1,y+1/2', 'x+5/4,-z+3/4,y+3/4', 'z+1/2,-x+1/2,-y', 'x+3/4,z+3/4,-y+1/4', '-z+1/2,x+1,-y+1/2', '-x+5/4,-z+3/4,-y+3/4', 'y+1/2,z+1/2,x', 'y+1,-z+1/2,-x+1/2', 'z+3/4,y+5/4,-x+3/4', '-y+1,z+1,-x', '-z+3/4,-y+3/4,-x+1/4', '-y+1/2,-z+1/2,x', 'z+3/4,-y+5/4,x+3/4', '-z+5/4,y+5/4,x+1/4'], 'universal_h_m': 'F4132'}, {'hall': ' I 4 2 3', 'hermann_mauguin': 'I432', 'hermann_mauguin_u': 'I432', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x'], 'number': 211, 'point_group': '432', 'schoenflies': 'O^5', 'short_h_m': 'I432', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z+1/2,x+1/2,y+1/2', '-x+1/2,z+1/2,y+1/2', '-z+1/2,-x+1/2,y+1/2', 'x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,-y+1/2', 'x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1/2', 'z+1/2,y+1/2,-x+1/2', '-y+1/2,z+1/2,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x+1/2', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2'], 'universal_h_m': 'I432'}, {'hall': ' P 4acd 2ab 3', 'hermann_mauguin': 'P4332', 'hermann_mauguin_u': 'P4_332', 'ncsym': ['x,y,z', '-y+3/4,x+1/4,z+3/4', '-x+1/2,-y,z+1/2', 'y+3/4,-x+3/4,z+1/4', 'x+1/2,-y+1/2,-z', 'y+1/4,x+3/4,-z+3/4', '-x,y+1/2,-z+1/2', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+3/4,z+1/4,y+3/4', '-z+1/2,-x,y+1/2', 'x+3/4,-z+3/4,y+1/4', 'z+1/2,-x+1/2,-y', 'x+1/4,z+3/4,-y+3/4', '-z,x+1/2,-y+1/2', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+1/4,y+3/4,-x+3/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4'], 'number': 212, 'point_group': '432', 'schoenflies': 'O^6', 'short_h_m': 'P4_332', 'symops': ['x,y,z', '-y+3/4,x+1/4,z+3/4', '-x+1/2,-y,z+1/2', 'y+3/4,-x+3/4,z+1/4', 'x+1/2,-y+1/2,-z', 'y+1/4,x+3/4,-z+3/4', '-x,y+1/2,-z+1/2', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+3/4,z+1/4,y+3/4', '-z+1/2,-x,y+1/2', 'x+3/4,-z+3/4,y+1/4', 'z+1/2,-x+1/2,-y', 'x+1/4,z+3/4,-y+3/4', '-z,x+1/2,-y+1/2', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+1/4,y+3/4,-x+3/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4'], 'universal_h_m': 'P4332'}, {'hall': ' P 4bd 2ab 3', 'hermann_mauguin': 'P4132', 'hermann_mauguin_u': 'P4_132', 'ncsym': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x+1/2,-y+1/2,-z', 'y+3/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+3/4,-z+3/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z+1/2,-x+1/2,-y', 'x+3/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+3/4,-y+3/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+3/4,-y+3/4,-x+3/4', '-y+1/2,-z,x+1/2', 'z+1/4,-y+1/4,x+3/4', '-z+1/4,y+3/4,x+1/4'], 'number': 213, 'point_group': '432', 'schoenflies': 'O^7', 'short_h_m': 'P4_132', 'symops': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x+1/2,-y+1/2,-z', 'y+3/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+3/4,-z+3/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z+1/2,-x+1/2,-y', 'x+3/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+3/4,-y+3/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+3/4,-y+3/4,-x+3/4', '-y+1/2,-z,x+1/2', 'z+1/4,-y+1/4,x+3/4', '-z+1/4,y+3/4,x+1/4'], 'universal_h_m': 'P4132'}, {'hall': ' I 4bd 2c 3', 'hermann_mauguin': 'I4132', 'hermann_mauguin_u': 'I4_132', 'ncsym': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z,-x,-y+1/2', 'x+1/4,z+3/4,-y+3/4', '-z+1/2,x,-y', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4'], 'number': 214, 'point_group': '432', 'schoenflies': 'O^8', 'short_h_m': 'I4_132', 'symops': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z,-x,-y+1/2', 'x+1/4,z+3/4,-y+3/4', '-z+1/2,x,-y', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4', 'x+1/2,y+1/2,z+1/2', '-y+3/4,x+5/4,z+3/4', '-x+1,-y+1/2,z+1', 'y+3/4,-x+3/4,z+5/4', 'x+1/2,-y+1/2,-z+1', 'y+3/4,x+5/4,-z+5/4', '-x+1,y+1/2,-z+1/2', '-y+3/4,-x+3/4,-z+3/4', 'z+1/2,x+1/2,y+1/2', '-x+3/4,z+5/4,y+3/4', '-z+1,-x+1/2,y+1', 'x+3/4,-z+3/4,y+5/4', 'z+1/2,-x+1/2,-y+1', 'x+3/4,z+5/4,-y+5/4', '-z+1,x+1/2,-y+1/2', '-x+3/4,-z+3/4,-y+3/4', 'y+1/2,z+1/2,x+1/2', 'y+1,-z+1,-x+1/2', 'z+5/4,y+3/4,-x+3/4', '-y+1/2,z+1,-x+1', '-z+3/4,-y+3/4,-x+3/4', '-y+1,-z+1/2,x+1', 'z+5/4,-y+5/4,x+3/4', '-z+5/4,y+3/4,x+5/4'], 'universal_h_m': 'I4132'}, {'hall': ' P -4 2 3', 'hermann_mauguin': 'P-43m', 'hermann_mauguin_u': 'P-43m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x'], 'number': 215, 'point_group': '-43m', 'schoenflies': 'Td^1', 'short_h_m': 'P-43m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x'], 'universal_h_m': 'P-43m'}, {'hall': ' F -4 2 3', 'hermann_mauguin': 'F-43m', 'hermann_mauguin_u': 'F-43m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x'], 'number': 216, 'point_group': '-43m', 'schoenflies': 'Td^2', 'short_h_m': 'F-43m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x', 'x,y+1/2,z+1/2', 'y,-x+1/2,-z+1/2', '-x,-y+1/2,z+1/2', '-y,x+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', '-y,-x+1/2,z+1/2', '-x,y+1/2,-z+1/2', 'y,x+1/2,z+1/2', 'z,x+1/2,y+1/2', 'x,-z+1/2,-y+1/2', '-z,-x+1/2,y+1/2', '-x,z+1/2,-y+1/2', 'z,-x+1/2,-y+1/2', '-x,-z+1/2,y+1/2', '-z,x+1/2,-y+1/2', 'x,z+1/2,y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', '-z,-y+1/2,x+1/2', '-y,z+1/2,-x+1/2', 'z,y+1/2,x+1/2', '-y,-z+1/2,x+1/2', '-z,y+1/2,-x+1/2', 'z,-y+1/2,-x+1/2', 'x+1/2,y,z+1/2', 'y+1/2,-x,-z+1/2', '-x+1/2,-y,z+1/2', '-y+1/2,x,-z+1/2', 'x+1/2,-y,-z+1/2', '-y+1/2,-x,z+1/2', '-x+1/2,y,-z+1/2', 'y+1/2,x,z+1/2', 'z+1/2,x,y+1/2', 'x+1/2,-z,-y+1/2', '-z+1/2,-x,y+1/2', '-x+1/2,z,-y+1/2', 'z+1/2,-x,-y+1/2', '-x+1/2,-z,y+1/2', '-z+1/2,x,-y+1/2', 'x+1/2,z,y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', '-z+1/2,-y,x+1/2', '-y+1/2,z,-x+1/2', 'z+1/2,y,x+1/2', '-y+1/2,-z,x+1/2', '-z+1/2,y,-x+1/2', 'z+1/2,-y,-x+1/2', 'x+1/2,y+1/2,z', 'y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,z', '-y+1/2,x+1/2,-z', 'x+1/2,-y+1/2,-z', '-y+1/2,-x+1/2,z', '-x+1/2,y+1/2,-z', 'y+1/2,x+1/2,z', 'z+1/2,x+1/2,y', 'x+1/2,-z+1/2,-y', '-z+1/2,-x+1/2,y', '-x+1/2,z+1/2,-y', 'z+1/2,-x+1/2,-y', '-x+1/2,-z+1/2,y', '-z+1/2,x+1/2,-y', 'x+1/2,z+1/2,y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', '-z+1/2,-y+1/2,x', '-y+1/2,z+1/2,-x', 'z+1/2,y+1/2,x', '-y+1/2,-z+1/2,x', '-z+1/2,y+1/2,-x', 'z+1/2,-y+1/2,-x'], 'universal_h_m': 'F-43m'}, {'hall': ' I -4 2 3', 'hermann_mauguin': 'I-43m', 'hermann_mauguin_u': 'I-43m', 'ncsym': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x'], 'number': 217, 'point_group': '-43m', 'schoenflies': 'Td^3', 'short_h_m': 'I-43m', 'symops': ['x,y,z', 'y,-x,-z', '-x,-y,z', '-y,x,-z', 'x,-y,-z', '-y,-x,z', '-x,y,-z', 'y,x,z', 'z,x,y', 'x,-z,-y', '-z,-x,y', '-x,z,-y', 'z,-x,-y', '-x,-z,y', '-z,x,-y', 'x,z,y', 'y,z,x', 'y,-z,-x', '-z,-y,x', '-y,z,-x', 'z,y,x', '-y,-z,x', '-z,y,-x', 'z,-y,-x', 'x+1/2,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', 'z+1/2,x+1/2,y+1/2', 'x+1/2,-z+1/2,-y+1/2', '-z+1/2,-x+1/2,y+1/2', '-x+1/2,z+1/2,-y+1/2', 'z+1/2,-x+1/2,-y+1/2', '-x+1/2,-z+1/2,y+1/2', '-z+1/2,x+1/2,-y+1/2', 'x+1/2,z+1/2,y+1/2', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1/2', '-z+1/2,-y+1/2,x+1/2', '-y+1/2,z+1/2,-x+1/2', 'z+1/2,y+1/2,x+1/2', '-y+1/2,-z+1/2,x+1/2', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'universal_h_m': 'I-43m'}, {'hall': ' P -4n 2 3', 'hermann_mauguin': 'P-43n', 'hermann_mauguin_u': 'P-43n', 'ncsym': ['x,y,z', 'y+1/2,-x+1/2,-z+1/2', '-x,-y,z', '-y+1/2,x+1/2,-z+1/2', 'x,-y,-z', '-y+1/2,-x+1/2,z+1/2', '-x,y,-z', 'y+1/2,x+1/2,z+1/2', 'z,x,y', 'x+1/2,-z+1/2,-y+1/2', '-z,-x,y', '-x+1/2,z+1/2,-y+1/2', 'z,-x,-y', '-x+1/2,-z+1/2,y+1/2', '-z,x,-y', 'x+1/2,z+1/2,y+1/2', 'y,z,x', 'y,-z,-x', '-z+1/2,-y+1/2,x+1/2', '-y,z,-x', 'z+1/2,y+1/2,x+1/2', '-y,-z,x', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'number': 218, 'point_group': '-43m', 'schoenflies': 'Td^4', 'short_h_m': 'P-43n', 'symops': ['x,y,z', 'y+1/2,-x+1/2,-z+1/2', '-x,-y,z', '-y+1/2,x+1/2,-z+1/2', 'x,-y,-z', '-y+1/2,-x+1/2,z+1/2', '-x,y,-z', 'y+1/2,x+1/2,z+1/2', 'z,x,y', 'x+1/2,-z+1/2,-y+1/2', '-z,-x,y', '-x+1/2,z+1/2,-y+1/2', 'z,-x,-y', '-x+1/2,-z+1/2,y+1/2', '-z,x,-y', 'x+1/2,z+1/2,y+1/2', 'y,z,x', 'y,-z,-x', '-z+1/2,-y+1/2,x+1/2', '-y,z,-x', 'z+1/2,y+1/2,x+1/2', '-y,-z,x', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'universal_h_m': 'P-43n'}, {'hall': ' F -4a 2 3', 'hermann_mauguin': 'F-43c', 'hermann_mauguin_u': 'F-43c', 'ncsym': ['x,y,z', 'y+1/2,-x,-z', '-x+1/2,-y+1/2,z', '-y,x+1/2,-z', 'x,-y,-z', '-y+1/2,-x,z', '-x+1/2,y+1/2,-z', 'y,x+1/2,z', 'z,x,y', 'x+1/2,-z,-y', '-z+1/2,-x+1/2,y', '-x,z+1/2,-y', 'z,-x,-y', '-x+1/2,-z,y', '-z+1/2,x+1/2,-y', 'x,z+1/2,y', 'y,z,x', 'y,-z+1/2,-x+1/2', '-z,-y,x+1/2', '-y+1/2,z,-x+1/2', 'z+1/2,y,x', '-y,-z,x', '-z,y,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'number': 219, 'point_group': '-43m', 'schoenflies': 'Td^5', 'short_h_m': 'F-43c', 'symops': ['x,y,z', 'y+1/2,-x,-z', '-x+1/2,-y+1/2,z', '-y,x+1/2,-z', 'x,-y,-z', '-y+1/2,-x,z', '-x+1/2,y+1/2,-z', 'y,x+1/2,z', 'z,x,y', 'x+1/2,-z,-y', '-z+1/2,-x+1/2,y', '-x,z+1/2,-y', 'z,-x,-y', '-x+1/2,-z,y', '-z+1/2,x+1/2,-y', 'x,z+1/2,y', 'y,z,x', 'y,-z+1/2,-x+1/2', '-z,-y,x+1/2', '-y+1/2,z,-x+1/2', 'z+1/2,y,x', '-y,-z,x', '-z,y,-x+1/2', 'z+1/2,-y+1/2,-x+1/2', 'x,y+1/2,z+1/2', 'y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1,z+1/2', '-y,x+1,-z+1/2', 'x,-y+1/2,-z+1/2', '-y+1/2,-x+1/2,z+1/2', '-x+1/2,y+1,-z+1/2', 'y,x+1,z+1/2', 'z,x+1/2,y+1/2', 'x+1/2,-z+1/2,-y+1/2', '-z+1/2,-x+1,y+1/2', '-x,z+1,-y+1/2', 'z,-x+1/2,-y+1/2', '-x+1/2,-z+1/2,y+1/2', '-z+1/2,x+1,-y+1/2', 'x,z+1,y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1,-x+1', '-z,-y+1/2,x+1', '-y+1/2,z+1/2,-x+1', 'z+1/2,y+1/2,x+1/2', '-y,-z+1/2,x+1/2', '-z,y+1/2,-x+1', 'z+1/2,-y+1,-x+1', 'x+1/2,y,z+1/2', 'y+1,-x,-z+1/2', '-x+1,-y+1/2,z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x+1/2,-y,-z+1/2', '-y+1,-x,z+1/2', '-x+1,y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', 'z+1/2,x,y+1/2', 'x+1,-z,-y+1/2', '-z+1,-x+1/2,y+1/2', '-x+1/2,z+1/2,-y+1/2', 'z+1/2,-x,-y+1/2', '-x+1,-z,y+1/2', '-z+1,x+1/2,-y+1/2', 'x+1/2,z+1/2,y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z+1/2,-x+1', '-z+1/2,-y,x+1', '-y+1,z,-x+1', 'z+1,y,x+1/2', '-y+1/2,-z,x+1/2', '-z+1/2,y,-x+1', 'z+1,-y+1/2,-x+1', 'x+1/2,y+1/2,z', 'y+1,-x+1/2,-z', '-x+1,-y+1,z', '-y+1/2,x+1,-z', 'x+1/2,-y+1/2,-z', '-y+1,-x+1/2,z', '-x+1,y+1,-z', 'y+1/2,x+1,z', 'z+1/2,x+1/2,y', 'x+1,-z+1/2,-y', '-z+1,-x+1,y', '-x+1/2,z+1,-y', 'z+1/2,-x+1/2,-y', '-x+1,-z+1/2,y', '-z+1,x+1,-y', 'x+1/2,z+1,y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1,-x+1/2', '-z+1/2,-y+1/2,x+1/2', '-y+1,z+1/2,-x+1/2', 'z+1,y+1/2,x', '-y+1/2,-z+1/2,x', '-z+1/2,y+1/2,-x+1/2', 'z+1,-y+1,-x+1/2'], 'universal_h_m': 'F-43c'}, {'hall': ' I -4bd 2c 3', 'hermann_mauguin': 'I-43d', 'hermann_mauguin_u': 'I-43d', 'ncsym': ['x,y,z', 'y+1/4,-x+3/4,-z+1/4', '-x,-y+1/2,z', '-y+3/4,x+3/4,-z+1/4', 'x,-y,-z+1/2', '-y+1/4,-x+3/4,z+3/4', '-x,y+1/2,-z+1/2', 'y+3/4,x+3/4,z+3/4', 'z,x,y', 'x+1/4,-z+3/4,-y+1/4', '-z,-x+1/2,y', '-x+3/4,z+3/4,-y+1/4', 'z,-x,-y+1/2', '-x+1/4,-z+3/4,y+3/4', '-z,x+1/2,-y+1/2', 'x+3/4,z+3/4,y+3/4', 'y,z,x', 'y,-z,-x+1/2', '-z+1/4,-y+3/4,x+3/4', '-y,z+1/2,-x+1/2', 'z+1/4,y+1/4,x+1/4', '-y+1/2,-z,x+1/2', '-z+1/4,y+1/4,-x+3/4', 'z+3/4,-y+1/4,-x+3/4'], 'number': 220, 'point_group': '-43m', 'schoenflies': 'Td^6', 'short_h_m': 'I-43d', 'symops': ['x,y,z', 'y+1/4,-x+3/4,-z+1/4', '-x,-y+1/2,z', '-y+3/4,x+3/4,-z+1/4', 'x,-y,-z+1/2', '-y+1/4,-x+3/4,z+3/4', '-x,y+1/2,-z+1/2', 'y+3/4,x+3/4,z+3/4', 'z,x,y', 'x+1/4,-z+3/4,-y+1/4', '-z,-x+1/2,y', '-x+3/4,z+3/4,-y+1/4', 'z,-x,-y+1/2', '-x+1/4,-z+3/4,y+3/4', '-z,x+1/2,-y+1/2', 'x+3/4,z+3/4,y+3/4', 'y,z,x', 'y,-z,-x+1/2', '-z+1/4,-y+3/4,x+3/4', '-y,z+1/2,-x+1/2', 'z+1/4,y+1/4,x+1/4', '-y+1/2,-z,x+1/2', '-z+1/4,y+1/4,-x+3/4', 'z+3/4,-y+1/4,-x+3/4', 'x+1/2,y+1/2,z+1/2', 'y+3/4,-x+5/4,-z+3/4', '-x+1/2,-y+1,z+1/2', '-y+5/4,x+5/4,-z+3/4', 'x+1/2,-y+1/2,-z+1', '-y+3/4,-x+5/4,z+5/4', '-x+1/2,y+1,-z+1', 'y+5/4,x+5/4,z+5/4', 'z+1/2,x+1/2,y+1/2', 'x+3/4,-z+5/4,-y+3/4', '-z+1/2,-x+1,y+1/2', '-x+5/4,z+5/4,-y+3/4', 'z+1/2,-x+1/2,-y+1', '-x+3/4,-z+5/4,y+5/4', '-z+1/2,x+1,-y+1', 'x+5/4,z+5/4,y+5/4', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1', '-z+3/4,-y+5/4,x+5/4', '-y+1/2,z+1,-x+1', 'z+3/4,y+3/4,x+3/4', '-y+1,-z+1/2,x+1', '-z+3/4,y+3/4,-x+5/4', 'z+5/4,-y+3/4,-x+5/4'], 'universal_h_m': 'I-43d'}, {'hall': '-P 4 2 3', 'hermann_mauguin': 'Pm-3m', 'hermann_mauguin_u': 'Pm-3m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x'], 'number': 221, 'point_group': 'm-3m', 'schoenflies': 'Oh^1', 'short_h_m': 'Pm-3m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x'], 'universal_h_m': 'Pm-3m'}, {'hall': ' P 4 2 3 -1n', 'hermann_mauguin': 'Pn-3n', 'hermann_mauguin_u': 'Pn-3n', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'x+1/2,-z+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', '-x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'number': 222, 'point_group': 'm-3m', 'schoenflies': 'Oh^2', 'short_h_m': 'Pn-3n', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'x+1/2,-z+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', '-x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'universal_h_m': 'Pn-3n:1'}, {'hall': '-P 4a 2bc 3', 'hermann_mauguin': 'Pn-3n', 'hermann_mauguin_u': 'Pn-3n', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x+1/2,-y+1/2', 'x,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x', '-z+1/2,y,x', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z-1/2', '-y,-x,z-1/2', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z-1/2', '-z,-x,-y', 'x-1/2,-z,-y', 'z-1/2,x-1/2,-y', '-x,z-1/2,-y', '-z,x-1/2,y-1/2', '-x,-z,y-1/2', 'z-1/2,-x,y-1/2', 'x-1/2,z-1/2,y-1/2', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z,-y,x-1/2', 'y-1/2,-z,x-1/2', 'z-1/2,y-1/2,x-1/2', 'y-1/2,z-1/2,-x', '-z,y-1/2,-x', 'z-1/2,-y,-x'], 'number': 222, 'point_group': 'm-3m', 'schoenflies': 'Oh^2', 'short_h_m': 'Pn-3n', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x+1/2,-y+1/2', 'x,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x', '-z+1/2,y,x', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y-1/2,z-1/2', '-y,-x,z-1/2', 'x-1/2,-y,z-1/2', 'y-1/2,x-1/2,z-1/2', '-z,-x,-y', 'x-1/2,-z,-y', 'z-1/2,x-1/2,-y', '-x,z-1/2,-y', '-z,x-1/2,y-1/2', '-x,-z,y-1/2', 'z-1/2,-x,y-1/2', 'x-1/2,z-1/2,y-1/2', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z,-y,x-1/2', 'y-1/2,-z,x-1/2', 'z-1/2,y-1/2,x-1/2', 'y-1/2,z-1/2,-x', '-z,y-1/2,-x', 'z-1/2,-y,-x'], 'universal_h_m': 'Pn-3n:2'}, {'hall': '-P 4n 2 3', 'hermann_mauguin': 'Pm-3n', 'hermann_mauguin_u': 'Pm-3n', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x,-y,-z', 'y-1/2,-x-1/2,-z-1/2', 'x,y,-z', '-y-1/2,x-1/2,-z-1/2', '-x,y,z', '-y-1/2,-x-1/2,z-1/2', 'x,-y,z', 'y-1/2,x-1/2,z-1/2', '-z,-x,-y', 'x-1/2,-z-1/2,-y-1/2', 'z,x,-y', '-x-1/2,z-1/2,-y-1/2', '-z,x,y', '-x-1/2,-z-1/2,y-1/2', 'z,-x,y', 'x-1/2,z-1/2,y-1/2', '-y,-z,-x', '-y,z,x', '-z-1/2,-y-1/2,x-1/2', 'y,-z,x', 'z-1/2,y-1/2,x-1/2', 'y,z,-x', '-z-1/2,y-1/2,-x-1/2', 'z-1/2,-y-1/2,-x-1/2'], 'number': 223, 'point_group': 'm-3m', 'schoenflies': 'Oh^3', 'short_h_m': 'Pm-3n', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x,-y,-z', 'y-1/2,-x-1/2,-z-1/2', 'x,y,-z', '-y-1/2,x-1/2,-z-1/2', '-x,y,z', '-y-1/2,-x-1/2,z-1/2', 'x,-y,z', 'y-1/2,x-1/2,z-1/2', '-z,-x,-y', 'x-1/2,-z-1/2,-y-1/2', 'z,x,-y', '-x-1/2,z-1/2,-y-1/2', '-z,x,y', '-x-1/2,-z-1/2,y-1/2', 'z,-x,y', 'x-1/2,z-1/2,y-1/2', '-y,-z,-x', '-y,z,x', '-z-1/2,-y-1/2,x-1/2', 'y,-z,x', 'z-1/2,y-1/2,x-1/2', 'y,z,-x', '-z-1/2,y-1/2,-x-1/2', 'z-1/2,-y-1/2,-x-1/2'], 'universal_h_m': 'Pm-3n'}, {'hall': ' P 4n 2 3 -1n', 'hermann_mauguin': 'Pn-3m', 'hermann_mauguin_u': 'Pn-3m', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z', '-z+1/2,-x+1/2,-y+1/2', 'x,-z,-y', 'z+1/2,x+1/2,-y+1/2', '-x,z,-y', '-z+1/2,x+1/2,y+1/2', '-x,-z,y', 'z+1/2,-x+1/2,y+1/2', 'x,z,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z,-y,x', 'y+1/2,-z+1/2,x+1/2', 'z,y,x', 'y+1/2,z+1/2,-x+1/2', '-z,y,-x', 'z,-y,-x'], 'number': 224, 'point_group': 'm-3m', 'schoenflies': 'Oh^4', 'short_h_m': 'Pn-3m', 'symops': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z', '-z+1/2,-x+1/2,-y+1/2', 'x,-z,-y', 'z+1/2,x+1/2,-y+1/2', '-x,z,-y', '-z+1/2,x+1/2,y+1/2', '-x,-z,y', 'z+1/2,-x+1/2,y+1/2', 'x,z,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z,-y,x', 'y+1/2,-z+1/2,x+1/2', 'z,y,x', 'y+1/2,z+1/2,-x+1/2', '-z,y,-x', 'z,-y,-x'], 'universal_h_m': 'Pn-3m:1'}, {'hall': '-P 4bc 2bc 3', 'hermann_mauguin': 'Pn-3m', 'hermann_mauguin_u': 'Pn-3m', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z+1/2', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z', '-x+1/2,y,-z+1/2', '-y,-x,-z', 'z,x,y', '-x,z+1/2,y+1/2', '-z+1/2,-x+1/2,y', 'x+1/2,-z,y+1/2', 'z,-x+1/2,-y+1/2', 'x+1/2,z+1/2,-y', '-z+1/2,x,-y+1/2', '-x,-z,-y', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z+1/2,y+1/2,-x', '-y+1/2,z,-x+1/2', '-z,-y,-x', '-y+1/2,-z+1/2,x', 'z+1/2,-y,x+1/2', '-z,y+1/2,x+1/2', '-x,-y,-z', 'y,-x-1/2,-z-1/2', 'x-1/2,y-1/2,-z', '-y-1/2,x,-z-1/2', '-x,y-1/2,z-1/2', '-y-1/2,-x-1/2,z', 'x-1/2,-y,z-1/2', 'y,x,z', '-z,-x,-y', 'x,-z-1/2,-y-1/2', 'z-1/2,x-1/2,-y', '-x-1/2,z,-y-1/2', '-z,x-1/2,y-1/2', '-x-1/2,-z-1/2,y', 'z-1/2,-x,y-1/2', 'x,z,y', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z-1/2,-y-1/2,x', 'y-1/2,-z,x-1/2', 'z,y,x', 'y-1/2,z-1/2,-x', '-z-1/2,y,-x-1/2', 'z,-y-1/2,-x-1/2'], 'number': 224, 'point_group': 'm-3m', 'schoenflies': 'Oh^4', 'short_h_m': 'Pn-3m', 'symops': ['x,y,z', '-y,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z+1/2', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z', '-x+1/2,y,-z+1/2', '-y,-x,-z', 'z,x,y', '-x,z+1/2,y+1/2', '-z+1/2,-x+1/2,y', 'x+1/2,-z,y+1/2', 'z,-x+1/2,-y+1/2', 'x+1/2,z+1/2,-y', '-z+1/2,x,-y+1/2', '-x,-z,-y', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z+1/2,y+1/2,-x', '-y+1/2,z,-x+1/2', '-z,-y,-x', '-y+1/2,-z+1/2,x', 'z+1/2,-y,x+1/2', '-z,y+1/2,x+1/2', '-x,-y,-z', 'y,-x-1/2,-z-1/2', 'x-1/2,y-1/2,-z', '-y-1/2,x,-z-1/2', '-x,y-1/2,z-1/2', '-y-1/2,-x-1/2,z', 'x-1/2,-y,z-1/2', 'y,x,z', '-z,-x,-y', 'x,-z-1/2,-y-1/2', 'z-1/2,x-1/2,-y', '-x-1/2,z,-y-1/2', '-z,x-1/2,y-1/2', '-x-1/2,-z-1/2,y', 'z-1/2,-x,y-1/2', 'x,z,y', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z-1/2,-y-1/2,x', 'y-1/2,-z,x-1/2', 'z,y,x', 'y-1/2,z-1/2,-x', '-z-1/2,y,-x-1/2', 'z,-y-1/2,-x-1/2'], 'universal_h_m': 'Pn-3m:2'}, {'hall': '-F 4 2 3', 'hermann_mauguin': 'Fm-3m', 'hermann_mauguin_u': 'Fm-3m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x'], 'number': 225, 'point_group': 'm-3m', 'schoenflies': 'Oh^5', 'short_h_m': 'Fm-3m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x+1/2,-z+1/2', 'z,x+1/2,y+1/2', '-x,z+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'x,-z+1/2,y+1/2', 'z,-x+1/2,-y+1/2', 'x,z+1/2,-y+1/2', '-z,x+1/2,-y+1/2', '-x,-z+1/2,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', 'z,y+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-z,-y+1/2,-x+1/2', '-y,-z+1/2,x+1/2', 'z,-y+1/2,x+1/2', '-z,y+1/2,x+1/2', '-x,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'y,x+1/2,z+1/2', '-z,-x+1/2,-y+1/2', 'x,-z+1/2,-y+1/2', 'z,x+1/2,-y+1/2', '-x,z+1/2,-y+1/2', '-z,x+1/2,y+1/2', '-x,-z+1/2,y+1/2', 'z,-x+1/2,y+1/2', 'x,z+1/2,y+1/2', '-y,-z+1/2,-x+1/2', '-y,z+1/2,x+1/2', '-z,-y+1/2,x+1/2', 'y,-z+1/2,x+1/2', 'z,y+1/2,x+1/2', 'y,z+1/2,-x+1/2', '-z,y+1/2,-x+1/2', 'z,-y+1/2,-x+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x,-z+1/2', 'z+1/2,x,y+1/2', '-x+1/2,z,y+1/2', '-z+1/2,-x,y+1/2', 'x+1/2,-z,y+1/2', 'z+1/2,-x,-y+1/2', 'x+1/2,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', 'z+1/2,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y,-x+1/2', '-y+1/2,-z,x+1/2', 'z+1/2,-y,x+1/2', '-z+1/2,y,x+1/2', '-x+1/2,-y,-z+1/2', 'y+1/2,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x,-z+1/2', '-x+1/2,y,z+1/2', '-y+1/2,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x,z+1/2', '-z+1/2,-x,-y+1/2', 'x+1/2,-z,-y+1/2', 'z+1/2,x,-y+1/2', '-x+1/2,z,-y+1/2', '-z+1/2,x,y+1/2', '-x+1/2,-z,y+1/2', 'z+1/2,-x,y+1/2', 'x+1/2,z,y+1/2', '-y+1/2,-z,-x+1/2', '-y+1/2,z,x+1/2', '-z+1/2,-y,x+1/2', 'y+1/2,-z,x+1/2', 'z+1/2,y,x+1/2', 'y+1/2,z,-x+1/2', '-z+1/2,y,-x+1/2', 'z+1/2,-y,-x+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-y+1/2,-x+1/2,-z', 'z+1/2,x+1/2,y', '-x+1/2,z+1/2,y', '-z+1/2,-x+1/2,y', 'x+1/2,-z+1/2,y', 'z+1/2,-x+1/2,-y', 'x+1/2,z+1/2,-y', '-z+1/2,x+1/2,-y', '-x+1/2,-z+1/2,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', 'z+1/2,y+1/2,-x', '-y+1/2,z+1/2,-x', '-z+1/2,-y+1/2,-x', '-y+1/2,-z+1/2,x', 'z+1/2,-y+1/2,x', '-z+1/2,y+1/2,x', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z', '-z+1/2,-x+1/2,-y', 'x+1/2,-z+1/2,-y', 'z+1/2,x+1/2,-y', '-x+1/2,z+1/2,-y', '-z+1/2,x+1/2,y', '-x+1/2,-z+1/2,y', 'z+1/2,-x+1/2,y', 'x+1/2,z+1/2,y', '-y+1/2,-z+1/2,-x', '-y+1/2,z+1/2,x', '-z+1/2,-y+1/2,x', 'y+1/2,-z+1/2,x', 'z+1/2,y+1/2,x', 'y+1/2,z+1/2,-x', '-z+1/2,y+1/2,-x', 'z+1/2,-y+1/2,-x'], 'universal_h_m': 'Fm-3m'}, {'hall': '-F 4a 2 3', 'hermann_mauguin': 'Fm-3c', 'hermann_mauguin_u': 'Fm-3c', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y,-z', 'y+1/2,x,-z', '-x+1/2,y+1/2,-z', '-y,-x+1/2,-z', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x,-y', 'x+1/2,z,-y', '-z+1/2,x+1/2,-y', '-x,-z+1/2,-y', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y,-x', '-y,-z,x', 'z,-y,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y,z', '-y-1/2,-x,z', 'x-1/2,-y-1/2,z', 'y,x-1/2,z', '-z,-x,-y', 'x-1/2,-z,-y', 'z-1/2,x-1/2,-y', '-x,z-1/2,-y', '-z,x,y', '-x-1/2,-z,y', 'z-1/2,-x-1/2,y', 'x,z-1/2,y', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z,-y,x-1/2', 'y-1/2,-z,x-1/2', 'z-1/2,y,x', 'y,z,-x', '-z,y,-x-1/2', 'z-1/2,-y-1/2,-x-1/2'], 'number': 226, 'point_group': 'm-3m', 'schoenflies': 'Oh^6', 'short_h_m': 'Fm-3c', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y,-z', 'y+1/2,x,-z', '-x+1/2,y+1/2,-z', '-y,-x+1/2,-z', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x,-y', 'x+1/2,z,-y', '-z+1/2,x+1/2,-y', '-x,-z+1/2,-y', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y,-x', '-y,-z,x', 'z,-y,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x,-y,-z', 'y-1/2,-x,-z', 'x-1/2,y-1/2,-z', '-y,x-1/2,-z', '-x,y,z', '-y-1/2,-x,z', 'x-1/2,-y-1/2,z', 'y,x-1/2,z', '-z,-x,-y', 'x-1/2,-z,-y', 'z-1/2,x-1/2,-y', '-x,z-1/2,-y', '-z,x,y', '-x-1/2,-z,y', 'z-1/2,-x-1/2,y', 'x,z-1/2,y', '-y,-z,-x', '-y,z-1/2,x-1/2', '-z,-y,x-1/2', 'y-1/2,-z,x-1/2', 'z-1/2,y,x', 'y,z,-x', '-z,y,-x-1/2', 'z-1/2,-y-1/2,-x-1/2', 'x,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1,z+1/2', 'y,-x+1,z+1/2', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1,-z+1/2', '-y,-x+1,-z+1/2', 'z,x+1/2,y+1/2', '-x+1/2,z+1/2,y+1/2', '-z+1/2,-x+1,y+1/2', 'x,-z+1,y+1/2', 'z,-x+1/2,-y+1/2', 'x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1,-y+1/2', '-x,-z+1,-y+1/2', 'y,z+1/2,x+1/2', 'y,-z+1,-x+1', 'z,y+1/2,-x+1', '-y+1/2,z+1/2,-x+1', '-z+1/2,-y+1/2,-x+1/2', '-y,-z+1/2,x+1/2', 'z,-y+1/2,x+1', '-z+1/2,y+1,x+1', '-x,-y+1/2,-z+1/2', 'y-1/2,-x+1/2,-z+1/2', 'x-1/2,y,-z+1/2', '-y,x,-z+1/2', '-x,y+1/2,z+1/2', '-y-1/2,-x+1/2,z+1/2', 'x-1/2,-y,z+1/2', 'y,x,z+1/2', '-z,-x+1/2,-y+1/2', 'x-1/2,-z+1/2,-y+1/2', 'z-1/2,x,-y+1/2', '-x,z,-y+1/2', '-z,x+1/2,y+1/2', '-x-1/2,-z+1/2,y+1/2', 'z-1/2,-x,y+1/2', 'x,z,y+1/2', '-y,-z+1/2,-x+1/2', '-y,z,x', '-z,-y+1/2,x', 'y-1/2,-z+1/2,x', 'z-1/2,y+1/2,x+1/2', 'y,z+1/2,-x+1/2', '-z,y+1/2,-x', 'z-1/2,-y,-x', 'x+1/2,y,z+1/2', '-y+1,x,z+1/2', '-x+1,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1,x,-z+1/2', '-x+1,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z+1/2,x,y+1/2', '-x+1,z,y+1/2', '-z+1,-x+1/2,y+1/2', 'x+1/2,-z+1/2,y+1/2', 'z+1/2,-x,-y+1/2', 'x+1,z,-y+1/2', '-z+1,x+1/2,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y+1/2,z,x+1/2', 'y+1/2,-z+1/2,-x+1', 'z+1/2,y,-x+1', '-y+1,z,-x+1', '-z+1,-y,-x+1/2', '-y+1/2,-z,x+1/2', 'z+1/2,-y,x+1', '-z+1,y+1/2,x+1', '-x+1/2,-y,-z+1/2', 'y,-x,-z+1/2', 'x,y-1/2,-z+1/2', '-y+1/2,x-1/2,-z+1/2', '-x+1/2,y,z+1/2', '-y,-x,z+1/2', 'x,-y-1/2,z+1/2', 'y+1/2,x-1/2,z+1/2', '-z+1/2,-x,-y+1/2', 'x,-z,-y+1/2', 'z,x-1/2,-y+1/2', '-x+1/2,z-1/2,-y+1/2', '-z+1/2,x,y+1/2', '-x,-z,y+1/2', 'z,-x-1/2,y+1/2', 'x+1/2,z-1/2,y+1/2', '-y+1/2,-z,-x+1/2', '-y+1/2,z-1/2,x', '-z+1/2,-y,x', 'y,-z,x', 'z,y,x+1/2', 'y+1/2,z,-x+1/2', '-z+1/2,y,-x', 'z,-y-1/2,-x', 'x+1/2,y+1/2,z', '-y+1,x+1/2,z', '-x+1,-y+1,z', 'y+1/2,-x+1,z', 'x+1/2,-y+1/2,-z', 'y+1,x+1/2,-z', '-x+1,y+1,-z', '-y+1/2,-x+1,-z', 'z+1/2,x+1/2,y', '-x+1,z+1/2,y', '-z+1,-x+1,y', 'x+1/2,-z+1,y', 'z+1/2,-x+1/2,-y', 'x+1,z+1/2,-y', '-z+1,x+1,-y', '-x+1/2,-z+1,-y', 'y+1/2,z+1/2,x', 'y+1/2,-z+1,-x+1/2', 'z+1/2,y+1/2,-x+1/2', '-y+1,z+1/2,-x+1/2', '-z+1,-y+1/2,-x', '-y+1/2,-z+1/2,x', 'z+1/2,-y+1/2,x+1/2', '-z+1,y+1,x+1/2', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y,-z', '-y+1/2,x,-z', '-x+1/2,y+1/2,z', '-y,-x+1/2,z', 'x,-y,z', 'y+1/2,x,z', '-z+1/2,-x+1/2,-y', 'x,-z+1/2,-y', 'z,x,-y', '-x+1/2,z,-y', '-z+1/2,x+1/2,y', '-x,-z+1/2,y', 'z,-x,y', 'x+1/2,z,y', '-y+1/2,-z+1/2,-x', '-y+1/2,z,x-1/2', '-z+1/2,-y+1/2,x-1/2', 'y,-z+1/2,x-1/2', 'z,y+1/2,x', 'y+1/2,z+1/2,-x', '-z+1/2,y+1/2,-x-1/2', 'z,-y,-x-1/2'], 'universal_h_m': 'Fm-3c'}, {'hall': ' F 4d 2 3 -1d', 'hermann_mauguin': 'Fd-3m', 'hermann_mauguin_u': 'Fd-3m', 'ncsym': ['x,y,z', '-y+1/4,x+1/4,z+1/4', '-x,-y+1/2,z+1/2', 'y+3/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+1/4,-z+3/4', 'z,x,y', '-x+1/4,z+1/4,y+1/4', '-z,-x+1/2,y+1/2', 'x+3/4,-z+1/4,y+3/4', 'z,-x,-y', 'x+1/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+1/4,-y+3/4', 'y,z,x', 'y+1/2,-z,-x+1/2', 'z+1/4,y+3/4,-x+3/4', '-y+1/2,z+1/2,-x', '-z+1/4,-y+1/4,-x+1/4', '-y,-z,x', 'z+1/4,-y+3/4,x+3/4', '-z+3/4,y+3/4,x+1/4', '-x+1/4,-y+1/4,-z+1/4', 'y,-x,-z', 'x+1/4,y-1/4,-z-1/4', '-y-1/2,x,-z-1/2', '-x+1/4,y+1/4,z+1/4', '-y,-x,z', 'x+1/4,-y-1/4,z-1/4', 'y-1/2,x,z-1/2', '-z+1/4,-x+1/4,-y+1/4', 'x,-z,-y', 'z+1/4,x-1/4,-y-1/4', '-x-1/2,z,-y-1/2', '-z+1/4,x+1/4,y+1/4', '-x,-z,y', 'z+1/4,-x-1/4,y-1/4', 'x-1/2,z,y-1/2', '-y+1/4,-z+1/4,-x+1/4', '-y-1/4,z+1/4,x-1/4', '-z,-y-1/2,x-1/2', 'y-1/4,-z-1/4,x+1/4', 'z,y,x', 'y+1/4,z+1/4,-x+1/4', '-z,y-1/2,-x-1/2', 'z-1/2,-y-1/2,-x'], 'number': 227, 'point_group': 'm-3m', 'schoenflies': 'Oh^7', 'short_h_m': 'Fd-3m', 'symops': ['x,y,z', '-y+1/4,x+1/4,z+1/4', '-x,-y+1/2,z+1/2', 'y+3/4,-x+1/4,z+3/4', 'x,-y,-z', 'y+1/4,x+1/4,-z+1/4', '-x,y+1/2,-z+1/2', '-y+3/4,-x+1/4,-z+3/4', 'z,x,y', '-x+1/4,z+1/4,y+1/4', '-z,-x+1/2,y+1/2', 'x+3/4,-z+1/4,y+3/4', 'z,-x,-y', 'x+1/4,z+1/4,-y+1/4', '-z,x+1/2,-y+1/2', '-x+3/4,-z+1/4,-y+3/4', 'y,z,x', 'y+1/2,-z,-x+1/2', 'z+1/4,y+3/4,-x+3/4', '-y+1/2,z+1/2,-x', '-z+1/4,-y+1/4,-x+1/4', '-y,-z,x', 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'-x,y-1/4,z-1/4', '-y-1/4,-x-1/4,z-1/2', 'x-1/4,-y-1/2,z-3/4', 'y,x-1/2,z', '-z,-x,-y', 'x-1/2,-z-1/4,-y-1/4', 'z-1/4,x-3/4,-y-1/2', '-x-3/4,z-1/2,-y-3/4', '-z,x-1/4,y-1/4', '-x-1/4,-z-1/4,y-1/2', 'z-1/4,-x-1/2,y-3/4', 'x,z-1/2,y', '-y,-z,-x', '-y-1/2,z-1/4,x-3/4', '-z-1/4,-y-3/4,x', 'y-3/4,-z-1/2,x-1/4', 'z-1/2,y-1/2,x-1/2', 'y-1/4,z-1/4,-x', '-z-1/4,y,-x-3/4', 'z,-y-3/4,-x-1/4'], 'number': 228, 'point_group': 'm-3m', 'schoenflies': 'Oh^8', 'short_h_m': 'Fd-3c', 'symops': ['x,y,z', '-y+1/2,x+1/4,z+1/4', '-x+1/4,-y+3/4,z+1/2', 'y+3/4,-x+1/2,z+3/4', 'x,-y+1/4,-z+1/4', 'y+1/4,x+1/4,-z+1/2', '-x+1/4,y+1/2,-z+3/4', '-y,-x+1/2,-z', 'z,x,y', '-x+1/2,z+1/4,y+1/4', '-z+1/4,-x+3/4,y+1/2', 'x+3/4,-z+1/2,y+3/4', 'z,-x+1/4,-y+1/4', 'x+1/4,z+1/4,-y+1/2', '-z+1/4,x+1/2,-y+3/4', '-x,-z+1/2,-y', 'y,z,x', 'y+1/2,-z+1/4,-x+3/4', 'z+1/4,y+3/4,-x', '-y+3/4,z+1/2,-x+1/4', '-z+1/2,-y+1/2,-x+1/2', '-y+1/4,-z+1/4,x', 'z+1/4,-y,x+3/4', '-z,y+3/4,x+1/4', '-x,-y,-z', 'y-1/2,-x-1/4,-z-1/4', 'x-1/4,y-3/4,-z-1/2', 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'-y-1/4,-x+1/4,z', 'x-1/4,-y,z-1/4', 'y,x,z+1/2', '-z,-x+1/2,-y+1/2', 'x-1/2,-z+1/4,-y+1/4', 'z-1/4,x-1/4,-y', '-x-3/4,z,-y-1/4', '-z,x+1/4,y+1/4', '-x-1/4,-z+1/4,y', 'z-1/4,-x,y-1/4', 'x,z,y+1/2', '-y,-z+1/2,-x+1/2', '-y-1/2,z+1/4,x-1/4', '-z-1/4,-y-1/4,x+1/2', 'y-3/4,-z,x+1/4', 'z-1/2,y,x', 'y-1/4,z+1/4,-x+1/2', '-z-1/4,y+1/2,-x-1/4', 'z,-y-1/4,-x+1/4', 'x+1/2,y,z+1/2', '-y+1,x+1/4,z+3/4', '-x+3/4,-y+3/4,z+1', 'y+5/4,-x+1/2,z+5/4', 'x+1/2,-y+1/4,-z+3/4', 'y+3/4,x+1/4,-z+1', '-x+3/4,y+1/2,-z+5/4', '-y+1/2,-x+1/2,-z+1/2', 'z+1/2,x,y+1/2', '-x+1,z+1/4,y+3/4', '-z+3/4,-x+3/4,y+1', 'x+5/4,-z+1/2,y+5/4', 'z+1/2,-x+1/4,-y+3/4', 'x+3/4,z+1/4,-y+1', '-z+3/4,x+1/2,-y+5/4', '-x+1/2,-z+1/2,-y+1/2', 'y+1/2,z,x+1/2', 'y+1,-z+1/4,-x+5/4', 'z+3/4,y+3/4,-x+1/2', '-y+5/4,z+1/2,-x+3/4', '-z+1,-y+1/2,-x+1', '-y+3/4,-z+1/4,x+1/2', 'z+3/4,-y,x+5/4', '-z+1/2,y+3/4,x+3/4', '-x+1/2,-y,-z+1/2', 'y,-x-1/4,-z+1/4', 'x+1/4,y-3/4,-z', '-y-1/4,x-1/2,-z-1/4', '-x+1/2,y-1/4,z+1/4', '-y+1/4,-x-1/4,z', 'x+1/4,-y-1/2,z-1/4', 'y+1/2,x-1/2,z+1/2', '-z+1/2,-x,-y+1/2', 'x,-z-1/4,-y+1/4', 'z+1/4,x-3/4,-y', '-x-1/4,z-1/2,-y-1/4', '-z+1/2,x-1/4,y+1/4', '-x+1/4,-z-1/4,y', 'z+1/4,-x-1/2,y-1/4', 'x+1/2,z-1/2,y+1/2', '-y+1/2,-z,-x+1/2', '-y,z-1/4,x-1/4', '-z+1/4,-y-3/4,x+1/2', 'y-1/4,-z-1/2,x+1/4', 'z,y-1/2,x', 'y+1/4,z-1/4,-x+1/2', '-z+1/4,y,-x-1/4', 'z+1/2,-y-3/4,-x+1/4', 'x+1/2,y+1/2,z', '-y+1,x+3/4,z+1/4', '-x+3/4,-y+5/4,z+1/2', 'y+5/4,-x+1,z+3/4', 'x+1/2,-y+3/4,-z+1/4', 'y+3/4,x+3/4,-z+1/2', '-x+3/4,y+1,-z+3/4', '-y+1/2,-x+1,-z', 'z+1/2,x+1/2,y', '-x+1,z+3/4,y+1/4', '-z+3/4,-x+5/4,y+1/2', 'x+5/4,-z+1,y+3/4', 'z+1/2,-x+3/4,-y+1/4', 'x+3/4,z+3/4,-y+1/2', '-z+3/4,x+1,-y+3/4', '-x+1/2,-z+1,-y', 'y+1/2,z+1/2,x', 'y+1,-z+3/4,-x+3/4', 'z+3/4,y+5/4,-x', '-y+5/4,z+1,-x+1/4', '-z+1,-y+1,-x+1/2', '-y+3/4,-z+3/4,x', 'z+3/4,-y+1/2,x+3/4', '-z+1/2,y+5/4,x+1/4', '-x+1/2,-y+1/2,-z', 'y,-x+1/4,-z-1/4', 'x+1/4,y-1/4,-z-1/2', '-y-1/4,x,-z-3/4', '-x+1/2,y+1/4,z-1/4', '-y+1/4,-x+1/4,z-1/2', 'x+1/4,-y,z-3/4', 'y+1/2,x,z', '-z+1/2,-x+1/2,-y', 'x,-z+1/4,-y-1/4', 'z+1/4,x-1/4,-y-1/2', '-x-1/4,z,-y-3/4', '-z+1/2,x+1/4,y-1/4', '-x+1/4,-z+1/4,y-1/2', 'z+1/4,-x,y-3/4', 'x+1/2,z,y', '-y+1/2,-z+1/2,-x', '-y,z+1/4,x-3/4', '-z+1/4,-y-1/4,x', 'y-1/4,-z,x-1/4', 'z,y,x-1/2', 'y+1/4,z+1/4,-x', '-z+1/4,y+1/2,-x-3/4', 'z+1/2,-y-1/4,-x-1/4'], 'universal_h_m': 'Fd-3c:2'}, {'hall': '-I 4 2 3', 'hermann_mauguin': 'Im-3m', 'hermann_mauguin_u': 'Im-3m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x'], 'number': 229, 'point_group': 'm-3m', 'schoenflies': 'Oh^9', 'short_h_m': 'Im-3m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z', '-z,-x,-y', 'x,-z,-y', 'z,x,-y', '-x,z,-y', '-z,x,y', '-x,-z,y', 'z,-x,y', 'x,z,y', '-y,-z,-x', '-y,z,x', '-z,-y,x', 'y,-z,x', 'z,y,x', 'y,z,-x', '-z,y,-x', 'z,-y,-x', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z+1/2,x+1/2,y+1/2', '-x+1/2,z+1/2,y+1/2', '-z+1/2,-x+1/2,y+1/2', 'x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,-y+1/2', 'x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,-x+1/2', 'z+1/2,y+1/2,-x+1/2', '-y+1/2,z+1/2,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x+1/2', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'x+1/2,-z+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', '-x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'universal_h_m': 'Im-3m'}, {'hall': '-I 4bd 2c 3', 'hermann_mauguin': 'Ia-3d', 'hermann_mauguin_u': 'Ia-3d', 'ncsym': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z,-x,-y+1/2', 'x+1/4,z+3/4,-y+3/4', '-z+1/2,x,-y', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z-1/2', '-y-1/4,-x-3/4,z-3/4', 'x-1/2,-y,z', 'y-1/4,x-1/4,z-1/4', '-z,-x,-y', 'x-1/4,-z-3/4,-y-1/4', 'z-1/2,x,-y-1/2', '-x-1/4,z-1/4,-y-3/4', '-z,x,y-1/2', '-x-1/4,-z-3/4,y-3/4', 'z-1/2,-x,y', 'x-1/4,z-1/4,y-1/4', '-y,-z,-x', '-y-1/2,z-1/2,x', '-z-3/4,-y-1/4,x-1/4', 'y,-z-1/2,x-1/2', 'z-1/4,y-1/4,x-1/4', 'y-1/2,z,-x-1/2', '-z-3/4,y-3/4,-x-1/4', 'z-3/4,-y-1/4,-x-3/4'], 'number': 230, 'point_group': 'm-3m', 'schoenflies': 'Oh^10', 'short_h_m': 'Ia-3d', 'symops': ['x,y,z', '-y+1/4,x+3/4,z+1/4', '-x+1/2,-y,z+1/2', 'y+1/4,-x+1/4,z+3/4', 'x,-y,-z+1/2', 'y+1/4,x+3/4,-z+3/4', '-x+1/2,y,-z', '-y+1/4,-x+1/4,-z+1/4', 'z,x,y', '-x+1/4,z+3/4,y+1/4', '-z+1/2,-x,y+1/2', 'x+1/4,-z+1/4,y+3/4', 'z,-x,-y+1/2', 'x+1/4,z+3/4,-y+3/4', '-z+1/2,x,-y', '-x+1/4,-z+1/4,-y+1/4', 'y,z,x', 'y+1/2,-z+1/2,-x', 'z+3/4,y+1/4,-x+1/4', '-y,z+1/2,-x+1/2', '-z+1/4,-y+1/4,-x+1/4', '-y+1/2,-z,x+1/2', 'z+3/4,-y+3/4,x+1/4', '-z+3/4,y+1/4,x+3/4', '-x,-y,-z', 'y-1/4,-x-3/4,-z-1/4', 'x-1/2,y,-z-1/2', '-y-1/4,x-1/4,-z-3/4', '-x,y,z-1/2', '-y-1/4,-x-3/4,z-3/4', 'x-1/2,-y,z', 'y-1/4,x-1/4,z-1/4', '-z,-x,-y', 'x-1/4,-z-3/4,-y-1/4', 'z-1/2,x,-y-1/2', '-x-1/4,z-1/4,-y-3/4', '-z,x,y-1/2', '-x-1/4,-z-3/4,y-3/4', 'z-1/2,-x,y', 'x-1/4,z-1/4,y-1/4', '-y,-z,-x', '-y-1/2,z-1/2,x', '-z-3/4,-y-1/4,x-1/4', 'y,-z-1/2,x-1/2', 'z-1/4,y-1/4,x-1/4', 'y-1/2,z,-x-1/2', '-z-3/4,y-3/4,-x-1/4', 'z-3/4,-y-1/4,-x-3/4', 'x+1/2,y+1/2,z+1/2', '-y+3/4,x+5/4,z+3/4', '-x+1,-y+1/2,z+1', 'y+3/4,-x+3/4,z+5/4', 'x+1/2,-y+1/2,-z+1', 'y+3/4,x+5/4,-z+5/4', '-x+1,y+1/2,-z+1/2', '-y+3/4,-x+3/4,-z+3/4', 'z+1/2,x+1/2,y+1/2', '-x+3/4,z+5/4,y+3/4', '-z+1,-x+1/2,y+1', 'x+3/4,-z+3/4,y+5/4', 'z+1/2,-x+1/2,-y+1', 'x+3/4,z+5/4,-y+5/4', '-z+1,x+1/2,-y+1/2', '-x+3/4,-z+3/4,-y+3/4', 'y+1/2,z+1/2,x+1/2', 'y+1,-z+1,-x+1/2', 'z+5/4,y+3/4,-x+3/4', '-y+1/2,z+1,-x+1', '-z+3/4,-y+3/4,-x+3/4', '-y+1,-z+1/2,x+1', 'z+5/4,-y+5/4,x+3/4', '-z+5/4,y+3/4,x+5/4', '-x+1/2,-y+1/2,-z+1/2', 'y+1/4,-x-1/4,-z+1/4', 'x,y+1/2,-z', '-y+1/4,x+1/4,-z-1/4', '-x+1/2,y+1/2,z', '-y+1/4,-x-1/4,z-1/4', 'x,-y+1/2,z+1/2', 'y+1/4,x+1/4,z+1/4', '-z+1/2,-x+1/2,-y+1/2', 'x+1/4,-z-1/4,-y+1/4', 'z,x+1/2,-y', '-x+1/4,z+1/4,-y-1/4', '-z+1/2,x+1/2,y', '-x+1/4,-z-1/4,y-1/4', 'z,-x+1/2,y+1/2', 'x+1/4,z+1/4,y+1/4', '-y+1/2,-z+1/2,-x+1/2', '-y,z,x+1/2', '-z-1/4,-y+1/4,x+1/4', 'y+1/2,-z,x', 'z+1/4,y+1/4,x+1/4', 'y,z+1/2,-x', '-z-1/4,y-1/4,-x+1/4', 'z-1/4,-y+1/4,-x-1/4'], 'universal_h_m': 'Ia-3d'}, {'hall': 'P 1 (1/2*x+1/2*y,1/2*x-1/2*y,-z)', 'hermann_mauguin': 'C1', 'hermann_mauguin_u': 'C1', 'ncsym': ['x, y, z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'C1', 'symops': ['x,y,z', '1/2+x,1/2+y,z'], 'universal_h_m': 'C1'}, {'hall': '-P 1 (-x,-1/2*y+1/2*z,1/2*y+1/2*z)', 'hermann_mauguin': 'A-1', 'hermann_mauguin_u': 'A-1', 'ncsym': ['x, y, z', '-x, -y, -z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'Ci^1', 'short_h_m': 'A-1', 'symops': ['x,y,z', '-x,-y,-z', 'x,1/2+y,1/2+z', '-x,1/2-y,1/2-z'], 'universal_h_m': 'A-1'}, {'hall': '-P 1 (-1/2*x+1/2*z,-y,1/2*x+1/2*z)', 'hermann_mauguin': 'B-1', 'hermann_mauguin_u': 'B-1', 'ncsym': ['x, y, z', '-x, -y, -z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'Ci^1', 'short_h_m': 'B-1', 'symops': ['x, y, z', 'x+1/2, y, z+1/2', '-x, -y, -z', '-x+1/2, -y, -z+1/2'], 'universal_h_m': 'B-1'}, {'hall': '-P 1 (-1/2*x+1/2*y+1/2*z,1/2*x-1/2*y+1/2*z,1/2*x+1/2*y-1/2*z)', 'hermann_mauguin': 'I-1', 'hermann_mauguin_u': 'I-1', 'ncsym': ['x,y,z', '-x,-y,-z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'D2^4', 'short_h_m': 'I-1', 'symops': ['x,y,z', '1/2-x,1/2-y,1/2-z', '1/2+x,1/2+y,1/2+z', '-x,-y,-z'], 'universal_h_m': 'I-1'}, {'hall': '-C 2yc (x+y-16/3*z,-x+y+16/3*z,1/3*z)', 'hermann_mauguin': 'R12/c1', 'hermann_mauguin_u': 'R12/c1', 'ncsym': ['x, y, z', 'y, x, -z+1/2', '-x, -y, -z', '-y, -x, z-1/2'], 'number': 15, 'point_group': '2/m', 'schoenflies': 'C2h^6', 'short_h_m': 'R2/c', 'symops': ['x, y, z', 'y, x, -z+1/2', 'x+2/3, y+1/3, z+1/3', 'y+2/3, x+1/3, -z+5/6', 'x+1/3, y+2/3, z+2/3', 'y+1/3, x+2/3, -z+7/6', '-x, -y, -z', '-y, -x, z-1/2', '-x+2/3, -y+1/3, -z+1/3', '-y+2/3, -x+1/3, z-1/6', '-x+1/3, -y+2/3, -z+2/3', '-y+1/3, -x+2/3, z+1/6'], 'universal_h_m': 'R12/c1'}, {'hall': ' P 2ac 2ab (x,y,z+1/4)', 'hermann_mauguin': 'P212121', 'hermann_mauguin_u': 'P2_12_12_1', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x+1/2,-y,z+1/2'], 'number': 19, 'point_group': '222', 'schoenflies': 'D2^4', 'short_h_m': 'P2_12_12_1', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z', '-x+1/2,-y,z+1/2'], 'universal_h_m': 'P212121(originshiftx,y,z+1/4)'}, {'hall': 'P 2yb (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'B1211', 'hermann_mauguin_u': 'B12_11', 'ncsym': ['x, y, z', '-x, y+1/2, -z'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'B2_1', 'symops': ['x, y, z', '-x, y+1/2, -z', 'x+1/2, y, z+1/2', '-x+1/2, y+1/2, -z+1/2'], 'universal_h_m': 'B1211'}, {'hall': '-P 1 (1/2*x+1/2*y,1/2*x-1/2*y,-z)', 'hermann_mauguin': 'C-1', 'hermann_mauguin_u': 'C-1', 'ncsym': ['x, y, z', '-x, -y, -z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'Ci^1', 'short_h_m': 'C-1', 'symops': ['x, y, z', 'x+1/2, y+1/2, z', '-x, -y, -z', '-x+1/2, -y+1/2, -z'], 'universal_h_m': 'C-1'}, {'hall': '-P 2yb (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'B121/m1', 'hermann_mauguin_u': 'B12_1/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,-y-1/2,z+1/2'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'B2_1/m', 'symops': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y-1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,-y-1/2,z+1/2'], 'universal_h_m': 'B121/m1'}, {'hall': ' P 1 (-x,-1/2*y+1/2*z,1/2*y+1/2*z)', 'hermann_mauguin': 'P1', 'hermann_mauguin_u': 'P1', 'ncsym': ['x,y,z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'P1', 'symops': ['x,y,z', 'x,y+1/2,z+1/2'], 'universal_h_m': 'P1(-a,-b+c,b+c)'}, {'hall': ' P 1 (-1/2*x+1/2*z,-y,1/2*x+1/2*z)', 'hermann_mauguin': 'P1', 'hermann_mauguin_u': 'P1', 'ncsym': ['x,y,z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'P1', 'symops': ['x,y,z', 'x+1/2,y,z+1/2'], 'universal_h_m': 'P1(-a+c,-b,a+c)'}, {'hall': ' P 1 (-1/2*x+1/2*y+1/2*z,1/2*x-1/2*y+1/2*z,1/2*x+1/2*y-1/2*z)', 'hermann_mauguin': 'P1', 'hermann_mauguin_u': 'P1', 'ncsym': ['x,y,z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'P1', 'symops': ['x,y,z', 'x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'P1(b+c,a+c,a+b)'}, {'hall': ' P 1 (1/2*y+1/2*z,1/2*x+1/2*z,1/2*x+1/2*y)', 'hermann_mauguin': 'P1', 'hermann_mauguin_u': 'P1', 'ncsym': ['x,y,z'], 'number': 1, 'point_group': '1', 'schoenflies': 'C1^1', 'short_h_m': 'P1', 'symops': ['x,y,z', 'x,y+1/2,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,y+1/2,z'], 'universal_h_m': 'P1(-a+b+c,a-b+c,a+b-c)'}, {'hall': '-P 1 (1/2*y+1/2*z,1/2*x+1/2*z,1/2*x+1/2*y)', 'hermann_mauguin': 'P-1', 'hermann_mauguin_u': 'P-1', 'ncsym': ['x,y,z', '-x,-y,-z'], 'number': 2, 'point_group': '-1', 'schoenflies': 'Ci^1', 'short_h_m': 'P-1', 'symops': ['x,y,z', '-x,-y,-z', 'x,y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,-z'], 'universal_h_m': 'P-1(-a+b+c,a-b+c,a+b-c)'}, {'hall': ' P 2y (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P121', 'hermann_mauguin_u': 'P121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 3, 'point_group': '2', 'schoenflies': 'C2^1', 'short_h_m': 'P2', 'symops': ['x,y,z', '-x,y,-z', 'x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2'], 'universal_h_m': 'P121(2*a+c,b,c)'}, {'hall': ' C 2y (x-1/2*z,y,1/2*z)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,y,-z', 'x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'universal_h_m': 'C121(a,b,a+2*c)'}, {'hall': ' P 2y (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P121', 'hermann_mauguin_u': 'P121', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 3, 'point_group': '2', 'schoenflies': 'C2^1', 'short_h_m': 'P2', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z'], 'universal_h_m': 'P121(c,2*a+c,b)'}, {'hall': ' C 2y (1/2*z,x-1/2*z,y)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,-y,z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,-y,z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2'], 'universal_h_m': 'C121(a+2*c,a,b)'}, {'hall': ' C 2y (z,y+1/4,-x-1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y+1/2,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,y,-z+1/2', 'x,y+1/2,z+1/2', '-x,y+1/2,-z'], 'universal_h_m': 'C121(c-1/4,b-1/4,-a)'}, {'hall': ' C 2y (x+1/4,y+1/4,z)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y+1/2,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z'], 'universal_h_m': 'C121(a-1/4,b-1/4,c)'}, {'hall': ' C 2y (x+1/4,y+1/4,-x+z-1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y+1/2,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z'], 'universal_h_m': 'C121(a+c-1/4,b-1/4,c)'}, {'hall': ' C 2y (x-1/2*z+1/4,y+1/4,1/2*z)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,y+1/2,-z'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x+1/2,y,z+1/2', '-x,y,-z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'C121(a-1/4,b-1/4,a+2*c)'}, {'hall': ' C 2y (z,x+1/4,y+1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2'], 'universal_h_m': 'C121(c-1/4,a-1/4,b)'}, {'hall': ' C 2y (-x-1/4,z,y+1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,y,z+1/2', '-x,-y,z+1/2'], 'universal_h_m': 'C121(-a-1/4,c-1/4,b)'}, {'hall': ' P 2yb (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P1211', 'hermann_mauguin_u': 'P12_11', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'P2_1', 'symops': ['x,y,z', '-x,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P1211(c,2*a+c,b)'}, {'hall': ' C 2y (-x+z-1/4,x+1/4,y+1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2'], 'universal_h_m': 'C121(c-1/4,a+c-1/4,b)'}, {'hall': ' C 2y (1/2*z,x-1/2*z+1/4,y+1/4)', 'hermann_mauguin': 'C121', 'hermann_mauguin_u': 'C121', 'ncsym': ['x,y,z', '-x,-y,z+1/2'], 'number': 5, 'point_group': '2', 'schoenflies': 'C2^3', 'short_h_m': 'C2', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,y+1/2,z', '-x+1/2,-y,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'C121(a+2*c-1/4,a-1/4,b)'}, {'hall': ' P -2y (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P1m1', 'hermann_mauguin_u': 'P1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', 'x,-y,z', 'x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P1m1(2*a+c,b,c)'}, {'hall': ' C -2y (x-1/2*z,y,1/2*z)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,-y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y,z', 'x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'C1m1(a,b,a+2*c)'}, {'hall': ' P -2y (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P1m1', 'hermann_mauguin_u': 'P1m1', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'P1m1(c,2*a+c,b)'}, {'hall': ' C -2y (1/2*z,x-1/2*z,y)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,y,-z', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z', 'x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,y,-z+1/2'], 'universal_h_m': 'C1m1(a+2*c,a,b)'}, {'hall': ' P -2y (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P1m1', 'hermann_mauguin_u': 'P1m1', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 6, 'point_group': 'm', 'schoenflies': 'Cs^1', 'short_h_m': 'Pm', 'symops': ['x,y,z', '-x,y,z', 'x,y+1/2,z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'P1m1(b,c,2*a+c)'}, {'hall': ' C -2y (y,1/2*z,x-1/2*z)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', '-x,y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x,y,z', 'x,y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'C1m1(b,a+2*c,a)'}, {'hall': ' C -2y (z,y+1/4,-x-1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'C1m1(c-1/4,b-1/4,-a)'}, {'hall': ' P -2yc (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P1c1', 'hermann_mauguin_u': 'P1c1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pc', 'symops': ['x,y,z', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'universal_h_m': 'P1c1(2*a+c,b,c)'}, {'hall': ' C -2y (x-1/2*z+1/4,y+1/4,1/2*z)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,-y,z+1/2'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y+1/2,z', 'x+1/2,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'C1m1(a-1/4,b-1/4,a+2*c)'}, {'hall': ' C -2y (x+1/4,y+1/4,-x+z-1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x+1/2,-y,z+1/2'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'C1m1(a+c-1/4,b-1/4,c)'}, {'hall': ' C -2y (x+1/4,y+1/4,z)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x+1/2,-y,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'C1m1(a-1/4,b-1/4,c)'}, {'hall': ' C -2y (-x-1/4,z,y+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,y,-z'], 'universal_h_m': 'C1m1(-a-1/4,c-1/4,b)'}, {'hall': ' P -2yc (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P1c1', 'hermann_mauguin_u': 'P1c1', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pc', 'symops': ['x,y,z', 'x+1/2,y,-z', 'x+1/2,y+1/2,z', 'x,y+1/2,-z'], 'universal_h_m': 'P1c1(c,2*a+c,b)'}, {'hall': ' C -2y (1/2*z,x-1/2*z+1/4,y+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x+1/2,y,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z+1/2', 'x,y+1/2,z+1/2', 'x,y+1/2,-z', 'x+1/2,y,z+1/2', 'x+1/2,y,-z'], 'universal_h_m': 'C1m1(a+2*c-1/4,a-1/4,b)'}, {'hall': ' C -2y (-x+z-1/4,x+1/4,y+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'C1m1(c-1/4,a+c-1/4,b)'}, {'hall': ' C -2y (z,x+1/4,y+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', 'x,y+1/2,-z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', 'x,y,-z+1/2', 'x,y+1/2,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'C1m1(c-1/4,a-1/4,b)'}, {'hall': ' P -2yc (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P1c1', 'hermann_mauguin_u': 'P1c1', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 7, 'point_group': 'm', 'schoenflies': 'Cs^2', 'short_h_m': 'Pc', 'symops': ['x,y,z', '-x,y+1/2,z', 'x,y+1/2,z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'P1c1(b,c,2*a+c)'}, {'hall': ' C -2y (y+1/4,-x-1/4,z)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x+1/2,y,z', 'x+1/2,y+1/2,z', '-x,y+1/2,z'], 'universal_h_m': 'C1m1(b-1/4,-a-1/4,c)'}, {'hall': ' C -2y (y+1/4,1/2*z,x-1/2*z+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', '-x,y+1/2,z'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x+1/2,y,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,y,z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,z'], 'universal_h_m': 'C1m1(b-1/4,a+2*c-1/4,a)'}, {'hall': ' C -2y (y+1/4,-x+z-1/4,x+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', '-x,y+1/2,z+1/2'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x+1/2,y,z', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'C1m1(b-1/4,c-1/4,a+c)'}, {'hall': ' C -2y (y+1/4,z,x+1/4)', 'hermann_mauguin': 'C1m1', 'hermann_mauguin_u': 'C1m1', 'ncsym': ['x,y,z', '-x,y,z+1/2'], 'number': 8, 'point_group': 'm', 'schoenflies': 'Cs^3', 'short_h_m': 'Cm', 'symops': ['x,y,z', '-x+1/2,y,z', 'x+1/2,y,z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'C1m1(b-1/4,c-1/4,a)'}, {'hall': '-P 2y (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P12/m1', 'hermann_mauguin_u': 'P12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P12/m1(2*a+c,b,c)'}, {'hall': '-C 2y (x-1/2*z,y,1/2*z)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,-z', 'x,-y,z', 'x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'C12/m1(a,b,a+2*c)'}, {'hall': '-P 2y (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P12/m1', 'hermann_mauguin_u': 'P12/m1', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'P12/m1(c,2*a+c,b)'}, {'hall': '-C 2y (1/2*z,x-1/2*z,y)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,-y,z', '-x,-y,-z', 'x,y,-z', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', 'x,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2'], 'universal_h_m': 'C12/m1(a+2*c,a,b)'}, {'hall': '-P 2y (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P12/m1', 'hermann_mauguin_u': 'P12/m1', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 10, 'point_group': '2/m', 'schoenflies': 'C2h^1', 'short_h_m': 'P2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z', 'x,y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'P12/m1(b,c,2*a+c)'}, {'hall': '-C 2y (y,1/2*z,x-1/2*z)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y,-z', '-x,-y,-z', '-x,y,z', 'x,y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'C12/m1(b,a+2*c,a)'}, {'hall': '-C 2y (z,y-1/4,-x-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y+1/2,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y,z+1/2'], 'universal_h_m': 'C12/m1(c-1/4,b+1/4,-a)'}, {'hall': '-C 2y (x+1/4,y-1/4,z)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y+1/2,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,-y,z'], 'universal_h_m': 'C12/m1(a-1/4,b+1/4,c)'}, {'hall': '-C 2y (x+1/4,y-1/4,-x+z-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y+1/2,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'C12/m1(a+c-1/4,b+1/4,c)'}, {'hall': '-C 2y (x-1/2*z+1/4,y-1/4,1/2*z)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,y+1/2,-z', '-x,-y,-z', 'x,-y+1/2,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'x,-y+1/2,z', 'x+1/2,y,z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'C12/m1(a-1/4,b+1/4,a+2*c)'}, {'hall': '-C 2y (z,x+1/4,y-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,-y+1/2,-z+1/2', 'x,y,-z+1/2', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,-y,-z', 'x,y+1/2,-z'], 'universal_h_m': 'C12/m1(c-1/4,a+1/4,b)'}, {'hall': '-C 2y (-x-1/4,z,y-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x+1/2,-y,-z+1/2', 'x,y,-z+1/2', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', '-x,-y,-z', 'x+1/2,y,-z'], 'universal_h_m': 'C12/m1(-a-1/4,c+1/4,b)'}, {'hall': '-P 2yb (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P121/m1', 'hermann_mauguin_u': 'P12_1/m1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'P2_1/m', 'symops': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'P121/m1(c,2*a+c,b)'}, {'hall': '-C 2y (-x+z-1/4,x+1/4,y-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'C12/m1(c-1/4,a+c+1/4,b)'}, {'hall': '-C 2y (1/2*z,x-1/2*z+1/4,y-1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,-y,-z', 'x,y,-z+1/2'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,-y+1/2,-z+1/2', 'x,y,-z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z', '-x+1/2,-y,-z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,-y,-z', 'x,y+1/2,-z', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y,-z'], 'universal_h_m': 'C12/m1(a+2*c-1/4,a+1/4,b)'}, {'hall': '-P 2yb (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P121/m1', 'hermann_mauguin_u': 'P12_1/m1', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z'], 'number': 11, 'point_group': '2/m', 'schoenflies': 'C2h^2', 'short_h_m': 'P2_1/m', 'symops': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z', 'x,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'P121/m1(b,c,2*a+c)'}, {'hall': '-C 2y (y-1/4,z,x+1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+1/2,y,z', 'x+1/2,y,z+1/2', 'x+1/2,-y,-z', '-x,-y,-z', '-x,y,z+1/2'], 'universal_h_m': 'C12/m1(b-1/4,c+1/4,a)'}, {'hall': '-C 2y (y-1/4,-x-1/4,z)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+1/2,y,z', 'x+1/2,y+1/2,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x,y+1/2,z'], 'universal_h_m': 'C12/m1(b-1/4,-a+1/4,c)'}, {'hall': '-C 2y (y-1/4,-x+z-1/4,x+1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y,-z', '-x,-y,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'C12/m1(b-1/4,c+1/4,a+c)'}, {'hall': '-C 2y (y-1/4,1/2*z,x-1/2*z+1/4)', 'hermann_mauguin': 'C12/m1', 'hermann_mauguin_u': 'C12/m1', 'ncsym': ['x,y,z', 'x+1/2,-y,-z', '-x,-y,-z', '-x+1/2,y,z'], 'number': 12, 'point_group': '2/m', 'schoenflies': 'C2h^3', 'short_h_m': 'C2/m', 'symops': ['x,y,z', 'x,-y,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+1/2,y,z', 'x,y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,-y,-z', '-x,-y,-z', '-x,y,z+1/2', 'x+1/2,y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', '-x,y+1/2,z'], 'universal_h_m': 'C12/m1(b-1/4,a+2*c+1/4,a)'}, {'hall': '-P 2yc (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P12/c1', 'hermann_mauguin_u': 'P12/c1', 'ncsym': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z+1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,-y,z'], 'universal_h_m': 'P12/c1(2*a+c,b,c)'}, {'hall': '-P 2yc (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P12/c1', 'hermann_mauguin_u': 'P12/c1', 'ncsym': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x+1/2,y,-z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x,-y,-z', 'x+1/2,y,-z', 'x+1/2,y+1/2,z', '-x,-y+1/2,z', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z'], 'universal_h_m': 'P12/c1(c,2*a+c,b)'}, {'hall': '-P 2yc (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P12/c1', 'hermann_mauguin_u': 'P12/c1', 'ncsym': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y+1/2,z'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', 'x,-y+1/2,-z', '-x,-y,-z', '-x,y+1/2,z', 'x,y+1/2,z+1/2', 'x,-y,-z+1/2', '-x,-y+1/2,-z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'P12/c1(b,c,2*a+c)'}, {'hall': '-P 2ybc (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'P121/c1', 'hermann_mauguin_u': 'P12_1/c1', 'ncsym': ['x,y,z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,-y+1/2,z+1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P121/c1(2*a+c,b,c)'}, {'hall': '-P 2ybc (-1/2*x+z,1/2*x,y)', 'hermann_mauguin': 'P121/c1', 'hermann_mauguin_u': 'P12_1/c1', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,-y,-z', 'x+1/2,y,-z+1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,-y,-z', 'x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'P121/c1(c,2*a+c,b)'}, {'hall': '-P 2ybc (y,-1/2*x+z,1/2*x)', 'hermann_mauguin': 'P121/c1', 'hermann_mauguin_u': 'P12_1/c1', 'ncsym': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x+1/2,y+1/2,z'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y,-z', '-x+1/2,y+1/2,z', 'x,y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x,-y+1/2,-z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'P121/c1(b,c,2*a+c)'}, {'hall': ' A 2 -2 (x,y-1/4,z+1/4)', 'hermann_mauguin': 'Amm2', 'hermann_mauguin_u': 'Amm2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Amm2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Amm2(a,b+1/4,c-1/4)'}, {'hall': ' A 2 -2b (y-1/4,-x,z+1/4)', 'hermann_mauguin': 'Aem2', 'hermann_mauguin_u': 'Aem2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Aem2', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,z', '-x,y,z', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', 'x,-y,z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'Aem2(b,-a+1/4,c-1/4)'}, {'hall': ' I 2 -2a (x+1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'Ima2', 'hermann_mauguin_u': 'Ima2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ima2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,y,z', 'x+1/2,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'Ima2(a-1/4,b-1/4,c+1/4)'}, {'hall': ' F 2 -2 (x,y+1/4,z+1/4)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z', 'x,-y,z+1/2'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Fmm2(a,b-1/4,c-1/4)'}, {'hall': ' A 2 -2b (x,y-1/4,z+1/4)', 'hermann_mauguin': 'Aem2', 'hermann_mauguin_u': 'Aem2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Aem2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,y+1/2,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'Aem2(a,b+1/4,c-1/4)'}, {'hall': ' A 2 -2 (y-1/4,-x,z+1/4)', 'hermann_mauguin': 'Amm2', 'hermann_mauguin_u': 'Amm2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Amm2', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,z', '-x+1/2,y,z', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y,z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'Amm2(b,-a+1/4,c-1/4)'}, {'hall': ' I 2 -2a (y+1/4,-x-1/4,z-1/4)', 'hermann_mauguin': 'Ima2', 'hermann_mauguin_u': 'Ima2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ima2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'Ima2(b-1/4,-a-1/4,c+1/4)'}, {'hall': ' F 2 -2 (x-1/4,y,z-1/4)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y,z+1/2', 'x,-y,z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x+1/2,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', '-x,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z', '-x,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Fmm2(a+1/4,b,c+1/4)'}, {'hall': ' A 2 -2b (-x,z+1/4,y-1/4)', 'hermann_mauguin': 'Aem2', 'hermann_mauguin_u': 'Aem2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Aem2', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,y,z+1/2', 'x,y,-z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', '-x,y+1/2,z', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'Aem2(-a,c+1/4,b-1/4)'}, {'hall': ' A 2 -2 (y-1/4,z+1/4,x)', 'hermann_mauguin': 'Amm2', 'hermann_mauguin_u': 'Amm2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Amm2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x,y,-z', '-x+1/2,y,z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z'], 'universal_h_m': 'Amm2(b,c+1/4,a-1/4)'}, {'hall': ' I 2 -2a (y+1/4,z-1/4,x+1/4)', 'hermann_mauguin': 'Ima2', 'hermann_mauguin_u': 'Ima2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ima2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y,-z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z'], 'universal_h_m': 'Ima2(b-1/4,c-1/4,a+1/4)'}, {'hall': ' F 2 -2 (y+1/4,z+1/4,x)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z', '-x,y+1/2,-z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x,y,-z', '-x+1/2,y,z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,y,-z+1/2', 'x+1/2,y,-z+1/2', '-x,y,z+1/2'], 'universal_h_m': 'Fmm2(b,c-1/4,a-1/4)'}, {'hall': ' A 2 -2 (-x,z+1/4,y-1/4)', 'hermann_mauguin': 'Amm2', 'hermann_mauguin_u': 'Amm2', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 38, 'point_group': 'mm2', 'schoenflies': 'C2v^14', 'short_h_m': 'Amm2', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x,y,z', 'x,y,-z+1/2', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', '-x,y+1/2,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'Amm2(-a,c+1/4,b-1/4)'}, {'hall': ' A 2 -2b (y-1/4,z+1/4,x)', 'hermann_mauguin': 'Aem2', 'hermann_mauguin_u': 'Aem2', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 39, 'point_group': 'mm2', 'schoenflies': 'C2v^15', 'short_h_m': 'Aem2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x+1/2,y,-z', '-x,y,z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'Aem2(b,c+1/4,a-1/4)'}, {'hall': ' I 2 -2a (-x-1/4,z-1/4,y+1/4)', 'hermann_mauguin': 'Ima2', 'hermann_mauguin_u': 'Ima2', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 46, 'point_group': 'mm2', 'schoenflies': 'C2v^22', 'short_h_m': 'Ima2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,y,z', 'x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'Ima2(-a-1/4,c-1/4,b+1/4)'}, {'hall': ' F 2 -2 (y,z-1/4,x-1/4)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y,z', '-x,y+1/2,-z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x,y,-z+1/2', 'x,y,-z+1/2', '-x,y,z', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', 'x,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y,-z', 'x+1/2,y,-z', '-x+1/2,y,z+1/2'], 'universal_h_m': 'Fmm2(b+1/4,c,a+1/4)'}, {'hall': ' F 2 -2 (x-1/4,y-1/4,z+1/2)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x+1/2,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x,-y+1/2,z+1/2', '-x,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Fmm2(a+1/4,b+1/4,c+1/2)'}, {'hall': ' F 2 -2 (y-1/4,z+1/2,x-1/4)', 'hermann_mauguin': 'Fmm2', 'hermann_mauguin_u': 'Fmm2', 'ncsym': ['x,y,z', 'x,y+1/2,-z', '-x,y+1/2,z', '-x,y,-z'], 'number': 42, 'point_group': 'mm2', 'schoenflies': 'C2v^18', 'short_h_m': 'Fmm2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x+1/2,y+1/2,z', '-x,y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,y,-z', 'x+1/2,y,-z', '-x,y,z+1/2'], 'universal_h_m': 'Fmm2(b+1/4,c+1/4,a+1/2)'}, {'hall': ' C 2 -2 (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cmm2', 'hermann_mauguin_u': 'Cmm2', 'ncsym': ['x,y,z', '-x,-y,z', '-x+1/2,y,z', 'x+1/2,-y,z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'Cmm2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x+1/2,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-x,-y,z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Cmm2(a-1/4,b-1/4,c)'}, {'hall': ' C 2 -2 (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cmm2', 'hermann_mauguin_u': 'Cmm2', 'ncsym': ['x,y,z', 'x,y,-z+1/2', '-x,y,z+1/2', '-x,y,-z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'Cmm2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x+1/2,y,z+1/2', '-x,y,-z', 'x+1/2,y,-z', '-x,y,z+1/2'], 'universal_h_m': 'Cmm2(b-1/4,c-1/4,a)'}, {'hall': ' A 2 -2ab (x,y-1/4,z+1/4)', 'hermann_mauguin': 'Aea2', 'hermann_mauguin_u': 'Aea2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Aea2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x+1/2,y+1/2,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Aea2(a,b+1/4,c-1/4)'}, {'hall': ' C 2c -2 (y+1/4,-x-1/4,z)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z+1/2', 'x+1/2,-y,z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmc21(b-1/4,-a-1/4,c)'}, {'hall': ' I 2 -2c (x+1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'Iba2', 'hermann_mauguin_u': 'Iba2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'number': 45, 'point_group': 'mm2', 'schoenflies': 'C2v^21', 'short_h_m': 'Iba2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x+1/2,y,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Iba2(a-1/4,b-1/4,c+1/4)'}, {'hall': ' A 2 -2ab (y-1/4,-x,z+1/4)', 'hermann_mauguin': 'Aea2', 'hermann_mauguin_u': 'Aea2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y+1/2,z', 'x,-y+1/2,z+1/2'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Aea2', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y+1/2,z', '-x,y+1/2,z', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', 'x,-y+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Aea2(b,-a+1/4,c-1/4)'}, {'hall': ' C 2c -2 (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x,y+1/2,z', 'x,-y+1/2,z+1/2'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmc21(a-1/4,b-1/4,c)'}, {'hall': ' C 2c -2 (-x-1/4,z,y+1/4)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', '-x,y+1/2,-z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x,y+1/2,-z', '-x,y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmc21(-a-1/4,c-1/4,b)'}, {'hall': ' A 2 -2ab (y-1/4,z+1/4,x)', 'hermann_mauguin': 'Aea2', 'hermann_mauguin_u': 'Aea2', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', '-x,y+1/2,-z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Aea2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x+1/2,y,-z+1/2', '-x,y,z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Aea2(b,c+1/4,a-1/4)'}, {'hall': ' I 2 -2c (y+1/4,z-1/4,x+1/4)', 'hermann_mauguin': 'Iba2', 'hermann_mauguin_u': 'Iba2', 'ncsym': ['x,y,z', 'x,y+1/2,-z+1/2', '-x,y,z+1/2', '-x,y+1/2,-z'], 'number': 45, 'point_group': 'mm2', 'schoenflies': 'C2v^21', 'short_h_m': 'Iba2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z', 'x+1/2,y,-z', '-x,y,z+1/2'], 'universal_h_m': 'Iba2(b-1/4,c-1/4,a+1/4)'}, {'hall': ' A 2 -2ab (-x,z+1/4,y-1/4)', 'hermann_mauguin': 'Aea2', 'hermann_mauguin_u': 'Aea2', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y+1/2,z', '-x,y+1/2,-z'], 'number': 41, 'point_group': 'mm2', 'schoenflies': 'C2v^17', 'short_h_m': 'Aea2', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,y,-z', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Aea2(-a,c+1/4,b-1/4)'}, {'hall': ' C 2c -2 (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', 'x+1/2,y,-z', '-x+1/2,y+1/2,z', '-x,y+1/2,-z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y+1/2,-z', 'x+1/2,y,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmc21(b-1/4,c-1/4,a)'}, {'hall': ' C 2 -2c (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Ccc2', 'hermann_mauguin_u': 'Ccc2', 'ncsym': ['x,y,z', '-x,-y,z', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'number': 37, 'point_group': 'mm2', 'schoenflies': 'C2v^13', 'short_h_m': 'Ccc2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x+1/2,y,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Ccc2(a-1/4,b-1/4,c)'}, {'hall': ' C 2 -2c (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Ccc2', 'hermann_mauguin_u': 'Ccc2', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', '-x,y,-z'], 'number': 37, 'point_group': 'mm2', 'schoenflies': 'C2v^13', 'short_h_m': 'Ccc2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Ccc2(b-1/4,c-1/4,a)'}, {'hall': ' A 2 -2a (x-1/4,y-1/4,z+1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', '-x,y,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Ama2(a+1/4,b+1/4,c-1/4)'}, {'hall': ' C 2c -2 (x,y-1/4,z)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y,z', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmc21(a,b+1/4,c)'}, {'hall': ' I 2 -2 (x,y+1/4,z)', 'hermann_mauguin': 'Imm2', 'hermann_mauguin_u': 'Imm2', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Imm2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Imm2(a,b-1/4,c)'}, {'hall': ' A 2 -2a (y-1/4,-x+1/4,z+1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,z', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y,z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Ama2(b+1/4,-a+1/4,c-1/4)'}, {'hall': ' C 2c -2 (y-1/4,-x,z)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmc21(b,-a+1/4,c)'}, {'hall': ' I 2 -2 (x+1/4,y,z-1/4)', 'hermann_mauguin': 'Imm2', 'hermann_mauguin_u': 'Imm2', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Imm2', 'symops': ['x,y,z', '-x+1/2,-y,z', '-x+1/2,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Imm2(a-1/4,b,c+1/4)'}, {'hall': ' C 2c -2 (y-1/4,z,x)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', 'x,y,-z', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmc21(b,c+1/4,a)'}, {'hall': ' A 2 -2a (y-1/4,z+1/4,x-1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', 'x,y,-z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Ama2(b+1/4,c+1/4,a-1/4)'}, {'hall': ' I 2 -2 (y+1/4,z,x)', 'hermann_mauguin': 'Imm2', 'hermann_mauguin_u': 'Imm2', 'ncsym': ['x,y,z', 'x,y,-z', '-x,y+1/2,z+1/2', '-x,y+1/2,-z+1/2'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Imm2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x,y,-z', '-x+1/2,y,z', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Imm2(b,c-1/4,a)'}, {'hall': ' A 2 -2a (-x+1/4,z+1/4,y-1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x,y,z', '-x+1/2,y+1/2,-z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x,y,z', 'x+1/2,y,-z+1/2', 'x,y+1/2,z+1/2', '-x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Ama2(-a+1/4,c+1/4,b-1/4)'}, {'hall': ' C 2c -2 (-x,z,y-1/4)', 'hermann_mauguin': 'Cmc21', 'hermann_mauguin_u': 'Cmc2_1', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x,y,z', '-x+1/2,y+1/2,-z'], 'number': 36, 'point_group': 'mm2', 'schoenflies': 'C2v^12', 'short_h_m': 'Cmc2_1', 'symops': ['x,y,z', '-x,y+1/2,-z+1/2', '-x,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmc21(-a,c+1/4,b)'}, {'hall': ' I 2 -2 (y,z-1/4,x+1/4)', 'hermann_mauguin': 'Imm2', 'hermann_mauguin_u': 'Imm2', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z', '-x,y,z', '-x+1/2,y+1/2,-z'], 'number': 44, 'point_group': 'mm2', 'schoenflies': 'C2v^20', 'short_h_m': 'Imm2', 'symops': ['x,y,z', '-x,y,-z+1/2', 'x,y,-z+1/2', '-x,y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Imm2(b-1/4,c,a+1/4)'}, {'hall': ' A 2 -2a (x,y-1/4,z+1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x,-y+1/2,z', '-x+1/2,y,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Ama2(a,b+1/4,c-1/4)'}, {'hall': ' A 2 -2a (y-1/4,-x,z+1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', '-x,-y,z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,z', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Ama2(b,-a+1/4,c-1/4)'}, {'hall': ' A 2 -2a (y-1/4,z+1/4,x)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y,z+1/2', '-x,y+1/2,-z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x+1/2,y,-z', 'x,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,y+1/2,-z', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Ama2(b,c+1/4,a-1/4)'}, {'hall': ' A 2 -2a (-x,z+1/4,y-1/4)', 'hermann_mauguin': 'Ama2', 'hermann_mauguin_u': 'Ama2', 'ncsym': ['x,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z'], 'number': 40, 'point_group': 'mm2', 'schoenflies': 'C2v^16', 'short_h_m': 'Ama2', 'symops': ['x,y,z', '-x,y,-z+1/2', '-x+1/2,y,z', 'x+1/2,y,-z+1/2', 'x,y+1/2,z+1/2', '-x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Ama2(-a,c+1/4,b-1/4)'}, {'hall': '-C 2 2c (z+1/4,x,y)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,z', '-x+1/2,-y,-z', '-x+1/2,y,z', 'x+1/2,-y,z', 'x+1/2,y,-z', 'x,y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2'], 'universal_h_m': 'Cccm(c,a,b-1/4)'}, {'hall': '-C 2 2c (y,z+1/4,x)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,z', 'x,-y,-z', '-x,-y+1/2,-z', 'x,-y+1/2,z', 'x,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,y,z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2'], 'universal_h_m': 'Cccm(b,c,a-1/4)'}, {'hall': '-C 2 2c (x,y,z+1/4)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z+1/2', 'x,y,-z+1/2', '-x,y,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Cccm(a,b,c-1/4)'}, {'hall': '-F 2 2 (x+1/4,y+1/4,z+1/4)', 'hermann_mauguin': 'Fmmm', 'hermann_mauguin_u': 'Fmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 69, 'point_group': 'mmm', 'schoenflies': 'D2h^23', 'short_h_m': 'Fmmm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y,-z', '-x,-y+1/2,-z', 'x+1/2,y,-z', '-x,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Fmmm(a-1/4,b-1/4,c-1/4)'}, {'hall': '-C 2 2c (z,x+1/4,y+1/4)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,z', '-x,-y+1/2,-z+1/2', '-x,y,z', 'x+1/2,-y+1/2,z', 'x+1/2,y,-z+1/2', 'x,y+1/2,z+1/2', 'x,-y,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,z+1/2', '-x,-y,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cccm(c-1/4,a-1/4,b)'}, {'hall': '-C 2 2c (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,-y,z', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y,-z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,-y,-z', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cccm(b-1/4,c-1/4,a)'}, {'hall': '-C 2 2c (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cccm', 'hermann_mauguin_u': 'Cccm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 66, 'point_group': 'mmm', 'schoenflies': 'D2h^20', 'short_h_m': 'Cccm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y,-z', '-x+1/2,y,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cccm(a-1/4,b-1/4,c)'}, {'hall': '-I 2 2 (x-1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'Immm', 'hermann_mauguin_u': 'Immm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 71, 'point_group': 'mmm', 'schoenflies': 'D2h^25', 'short_h_m': 'Immm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Immm(a+1/4,b-1/4,c+1/4)'}, {'hall': '-F 2 2 (x-1/4,y-1/4,z)', 'hermann_mauguin': 'Fmmm', 'hermann_mauguin_u': 'Fmmm', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y,-z', '-x,y,z+1/2', 'x,-y,z+1/2'], 'number': 69, 'point_group': 'mmm', 'schoenflies': 'D2h^23', 'short_h_m': 'Fmmm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'x,y,-z', '-x+1/2,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,y,-z+1/2', '-x,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Fmmm(a+1/4,b+1/4,c)'}, {'hall': '-F 2 2 (x+1/2,y-1/4,z-1/4)', 'hermann_mauguin': 'Fmmm', 'hermann_mauguin_u': 'Fmmm', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x+1/2,y,-z', '-x,y,z', 'x+1/2,-y,z'], 'number': 69, 'point_group': 'mmm', 'schoenflies': 'D2h^23', 'short_h_m': 'Fmmm', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x,y,z', 'x,-y+1/2,z', 'x,y+1/2,z+1/2', '-x,-y,z+1/2', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x,y+1/2,-z', '-x,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y,-z', '-x+1/2,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Fmmm(a+1/2,b+1/4,c+1/4)'}, {'hall': '-F 2 2 (x+1/4,y+1/2,z-1/4)', 'hermann_mauguin': 'Fmmm', 'hermann_mauguin_u': 'Fmmm', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y,-z', 'x,y+1/2,-z', '-x,y+1/2,z', 'x,-y,z'], 'number': 69, 'point_group': 'mmm', 'schoenflies': 'D2h^23', 'short_h_m': 'Fmmm', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y,z', 'x,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x,y,-z', '-x,-y,-z', 'x+1/2,y,-z', '-x,y,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Fmmm(a-1/4,b+1/2,c+1/4)'}, {'hall': '-I 2 2c (x,y,z-1/4)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,-z+1/2', 'x,y,-z+1/2', '-x,y,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'Ibam(a,b,c+1/4)'}, {'hall': '-C 2 2 (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cmmm', 'hermann_mauguin_u': 'Cmmm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Cmmm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'x,y,-z', '-x+1/2,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-x,-y,z', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Cmmm(a-1/4,b-1/4,c)'}, {'hall': '-I 2 2c (x-1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,-y,z'], 'universal_h_m': 'Ibam(a+1/4,b-1/4,c+1/4)'}, {'hall': '-I 2 2c (z-1/4,x,y)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x,-y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', 'x,-y,-z', '-x,y,-z', '-x,-y,z', '-x+1/2,-y,-z', '-x+1/2,y,z', 'x+1/2,-y,z', 'x+1/2,y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x,y+1/2,-z+1/2'], 'universal_h_m': 'Ibam(c,a,b+1/4)'}, {'hall': '-C 2 2 (z,x+1/4,y+1/4)', 'hermann_mauguin': 'Cmmm', 'hermann_mauguin_u': 'Cmmm', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z', '-x,y+1/2,z+1/2', 'x,-y,z+1/2'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Cmmm', 'symops': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,z', '-x,-y+1/2,-z+1/2', '-x,y,z', 'x,-y+1/2,z', 'x,y,-z+1/2', 'x,y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z', '-x,-y,z+1/2', '-x,-y,-z', '-x,y+1/2,z+1/2', 'x,-y,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'Cmmm(c-1/4,a-1/4,b)'}, {'hall': '-I 2 2c (z-1/4,x-1/4,y+1/4)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z', '-x,y+1/2,z+1/2', 'x,-y,z+1/2'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', 'x,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,z', '-x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,z', 'x+1/2,-y+1/2,z', 'x+1/2,y,-z+1/2', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,z+1/2', '-x,-y,-z', '-x,y+1/2,z+1/2', 'x,-y,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'Ibam(c+1/4,a-1/4,b+1/4)'}, {'hall': '-I 2 2c (y,z-1/4,x)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', '-x,y,-z', '-x,-y,z', 'x,-y,-z', '-x,-y+1/2,-z', 'x,-y+1/2,z', 'x,y+1/2,-z', '-x,y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y,-z+1/2', '-x+1/2,y,z+1/2'], 'universal_h_m': 'Ibam(b,c,a+1/4)'}, {'hall': '-C 2 2 (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cmmm', 'hermann_mauguin_u': 'Cmmm', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y,-z', '-x,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 65, 'point_group': 'mmm', 'schoenflies': 'D2h^19', 'short_h_m': 'Cmmm', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,-y,z', 'x,y,-z+1/2', '-x+1/2,y,z', 'x+1/2,y,z+1/2', '-x,y,-z', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x,-y,-z', 'x+1/2,-y,z+1/2', 'x+1/2,y,-z', '-x,y,z+1/2'], 'universal_h_m': 'Cmmm(b-1/4,c-1/4,a)'}, {'hall': '-I 2 2c (y+1/4,z-1/4,x-1/4)', 'hermann_mauguin': 'Ibam', 'hermann_mauguin_u': 'Ibam', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y,-z', '-x,y,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 72, 'point_group': 'mmm', 'schoenflies': 'D2h^26', 'short_h_m': 'Ibam', 'symops': ['x,y,z', '-x+1/2,y,-z+1/2', '-x+1/2,-y,z', 'x,-y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'x,-y+1/2,z', 'x,y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x,y+1/2,-z', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,-y,-z', 'x+1/2,-y,z+1/2', 'x+1/2,y,-z', '-x,y,z+1/2'], 'universal_h_m': 'Ibam(b+1/4,c-1/4,a+1/4)'}, {'hall': '-C 2c 2 (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,z', 'x,-y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x,-y+1/2,z', 'x,y,-z+1/2', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y+1/2,-z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z', '-x,-y,-z', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y,-z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmcm(b-1/4,c-1/4,a)'}, {'hall': '-C 2c 2 (z,y+1/4,-x-1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,-y+1/2,z', '-x+1/2,y,-z+1/2', '-x,-y+1/2,-z+1/2', '-x+1/2,y,z', 'x,y,-z+1/2', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', 'x+1/2,-y,-z', '-x,-y,z+1/2', '-x+1/2,y+1/2,-z', '-x,-y,-z', '-x+1/2,y+1/2,z+1/2', 'x,y+1/2,-z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmcm(c-1/4,b-1/4,-a)'}, {'hall': '-C 2c 2 (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmcm(a-1/4,b-1/4,c)'}, {'hall': '-C 2c 2 (-x-1/4,z,y+1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z+1/2', 'x,-y,-z+1/2', '-x+1/2,-y+1/2,z', '-x+1/2,-y,-z+1/2', 'x,-y+1/2,z', '-x+1/2,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x,y+1/2,-z', 'x+1/2,-y,-z', '-x,-y+1/2,z+1/2', '-x,-y,-z', 'x+1/2,-y+1/2,z+1/2', '-x,y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmcm(-a-1/4,c-1/4,b)'}, {'hall': '-C 2c 2 (z,x+1/4,y+1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z+1/2', '-x,y,-z+1/2', '-x+1/2,-y+1/2,z', '-x,-y+1/2,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z', 'x+1/2,y,-z+1/2', 'x,y+1/2,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z', '-x+1/2,-y,z+1/2', '-x,-y,-z', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmcm(c-1/4,a-1/4,b)'}, {'hall': '-C 2c 2 (y+1/4,-x-1/4,z)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/2,y,-z', 'x,-y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y,-z+1/2', 'x,-y+1/2,z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y,z+1/2', '-x,y+1/2,-z', 'x+1/2,-y,-z+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y,z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmcm(b-1/4,-a-1/4,c)'}, {'hall': '-C 2ac 2 (z,x+1/4,y+1/4)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x+1/2,y,-z', '-x+1/2,y,z+1/2', 'x,-y,z+1/2'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x,y,-z+1/2', '-x+1/2,-y,z', '-x,-y+1/2,-z+1/2', '-x+1/2,y+1/2,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,-z+1/2', 'x,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y+1/2,-z', '-x+1/2,-y+1/2,z+1/2', '-x,-y,-z', '-x+1/2,y,z+1/2', 'x,-y,z+1/2', 'x+1/2,y,-z'], 'universal_h_m': 'Cmce(c-1/4,a-1/4,b)'}, {'hall': '-C 2ac 2 (-x-1/4,z,y+1/4)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x,-y,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z', '-x,y,z+1/2', 'x,-y+1/2,z+1/2'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', '-x,y+1/2,-z+1/2', 'x,-y,-z+1/2', '-x,-y+1/2,z', '-x+1/2,-y,-z+1/2', 'x+1/2,-y+1/2,z', '-x+1/2,y,z', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z', 'x+1/2,-y,-z', '-x+1/2,-y+1/2,z+1/2', '-x,-y,-z', 'x,-y+1/2,z+1/2', '-x,y,z+1/2', 'x,y+1/2,-z'], 'universal_h_m': 'Cmce(-a-1/4,c-1/4,b)'}, {'hall': '-C 2ac 2 (y+1/4,z,x+1/4)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y,-z', 'x+1/2,y,-z', '-x,y+1/2,z', 'x+1/2,-y+1/2,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,z', 'x,-y+1/2,-z', '-x+1/2,-y,-z+1/2', 'x,-y+1/2,z+1/2', 'x,y,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,-y+1/2,z', 'x+1/2,y,-z', '-x,y+1/2,z'], 'universal_h_m': 'Cmce(b-1/4,c-1/4,a)'}, {'hall': '-C 2ac 2 (y+1/4,-x-1/4,z)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x,-y,-z+1/2', '-x+1/2,y,-z', '-x,-y,-z', 'x+1/2,y,-z+1/2', '-x,y,z+1/2', 'x+1/2,-y,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', '-x+1/2,y,-z', 'x,-y,-z+1/2', '-x+1/2,-y+1/2,-z', 'x,y+1/2,-z+1/2', 'x,-y+1/2,z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,-z', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z', 'x+1/2,y,-z+1/2', 'x+1/2,-y,z', '-x,y,z+1/2'], 'universal_h_m': 'Cmce(b-1/4,-a-1/4,c)'}, {'hall': '-C 2ac 2 (x+1/4,y+1/4,z)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x,y,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z+1/2', '-x,y+1/2,z', 'x,-y,z+1/2'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z', '-x,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,y,-z+1/2', '-x+1/2,y,z', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', 'x,y+1/2,-z+1/2', '-x,y+1/2,z', 'x,-y,z+1/2'], 'universal_h_m': 'Cmce(a-1/4,b-1/4,c)'}, {'hall': '-C 2ac 2 (z,y+1/4,-x-1/4)', 'hermann_mauguin': 'Cmce', 'hermann_mauguin_u': 'Cmce', 'ncsym': ['x,y,z', '-x,-y+1/2,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y,-z', '-x,-y,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y,z'], 'number': 64, 'point_group': 'mmm', 'schoenflies': 'D2h^18', 'short_h_m': 'Cmce', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x,-y+1/2,z', '-x+1/2,y,-z', '-x,-y+1/2,-z+1/2', '-x+1/2,y,z+1/2', 'x,y,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x,-y,z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x,-y,-z', '-x+1/2,y+1/2,z', 'x,y+1/2,-z', 'x+1/2,-y,z'], 'universal_h_m': 'Cmce(c-1/4,b-1/4,-a)'}, {'hall': '-C 2c 2 (z-1/4,x+1/2,y+1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y,z', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', 'x+1/2,-y,-z+1/2', '-x+1/2,y,-z+1/2', '-x,-y,z', '-x+1/2,-y,-z+1/2', '-x,y,z', 'x,-y,z', 'x+1/2,y,-z+1/2', 'x,y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x,-y+1/2,z+1/2', '-x+1/2,-y+1/2,-z', '-x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmcm(c+1/2,a-1/4,b+1/4)'}, {'hall': '-C 2c 2 (-x+1/2,z-1/4,y+1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y,z', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x,y+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', '-x,-y,z', '-x,-y+1/2,-z+1/2', 'x,-y,z', '-x,y,z', 'x,y+1/2,-z+1/2', 'x+1/2,y,z+1/2', '-x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,-z', '-x+1/2,-y,z+1/2', '-x+1/2,-y+1/2,-z', 'x+1/2,-y,z+1/2', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Cmcm(-a+1/2,c-1/4,b+1/4)'}, {'hall': '-I 2 2 (x,y,z+1/4)', 'hermann_mauguin': 'Immm', 'hermann_mauguin_u': 'Immm', 'ncsym': ['x,y,z', '-x,-y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x,y,z', 'x,-y,z'], 'number': 71, 'point_group': 'mmm', 'schoenflies': 'D2h^25', 'short_h_m': 'Immm', 'symops': ['x,y,z', '-x,-y,z', 'x,-y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z+1/2', 'x,y,-z+1/2', '-x,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Immm(a,b,c-1/4)'}, {'hall': '-C 2c 2 (y+1/4,z-1/4,x+1/2)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,z', 'x,-y,-z', '-x+1/2,-y+1/2,-z', 'x,-y,z', 'x,y,-z', '-x+1/2,y+1/2,z', 'x+1/2,y,z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y,-z+1/2', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmcm(b+1/2,c-1/4,a+1/4)'}, {'hall': '-C 2c 2 (y+1/4,-x+1/2,z-1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x+1/2,-y,z+1/2', '-x+1/2,y,-z+1/2', 'x,-y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', 'x,-y,z', '-x+1/2,y,z+1/2', 'x+1/2,y+1/2,z', '-x,-y+1/2,z+1/2', '-x,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z', '-x,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z', 'x+1/2,-y+1/2,z', '-x,y+1/2,z+1/2'], 'universal_h_m': 'Cmcm(b+1/2,-a-1/4,c+1/4)'}, {'hall': '-I 2 2 (x+1/4,y,z)', 'hermann_mauguin': 'Immm', 'hermann_mauguin_u': 'Immm', 'ncsym': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y,-z', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y+1/2,z+1/2', 'x,-y,z'], 'number': 71, 'point_group': 'mmm', 'schoenflies': 'D2h^25', 'short_h_m': 'Immm', 'symops': ['x,y,z', '-x+1/2,-y,z', 'x,-y,-z', '-x+1/2,y,-z', '-x+1/2,-y,-z', 'x,y,-z', '-x+1/2,y,z', 'x,-y,z', 'x+1/2,y+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'Immm(a-1/4,b,c)'}, {'hall': '-C 2c 2 (z-1/4,y+1/4,-x+1/2)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', 'x+1/2,-y+1/2,-z', '-x+1/2,-y+1/2,z', '-x,y,-z', '-x+1/2,-y+1/2,-z', '-x,y,z', 'x,y,-z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,-y,z+1/2', '-x,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', '-x,y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmcm(c+1/2,b-1/4,-a+1/4)'}, {'hall': '-C 2c 2 (x+1/2,y+1/4,z-1/4)', 'hermann_mauguin': 'Cmcm', 'hermann_mauguin_u': 'Cmcm', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 63, 'point_group': 'mmm', 'schoenflies': 'D2h^17', 'short_h_m': 'Cmcm', 'symops': ['x,y,z', '-x,-y+1/2,z+1/2', 'x,-y+1/2,-z+1/2', '-x,y,-z', '-x,-y+1/2,-z+1/2', 'x,y,-z', '-x,y,z', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y,-z+1/2', 'x+1/2,y+1/2,-z', '-x+1/2,y+1/2,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Cmcm(a+1/2,b-1/4,c+1/4)'}, {'hall': '-I 2 2 (x,y+1/4,z)', 'hermann_mauguin': 'Immm', 'hermann_mauguin_u': 'Immm', 'ncsym': ['x,y,z', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x,y,-z', '-x+1/2,-y,-z+1/2', 'x,y,-z', '-x,y,z', 'x+1/2,-y,z+1/2'], 'number': 71, 'point_group': 'mmm', 'schoenflies': 'D2h^25', 'short_h_m': 'Immm', 'symops': ['x,y,z', '-x,-y+1/2,z', 'x,-y+1/2,-z', '-x,y,-z', '-x,-y+1/2,-z', 'x,y,-z', '-x,y,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', 'x+1/2,-y,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'Immm(a,b-1/4,c)'}, {'hall': '-I 4 (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', '-x+1/2,-y,-z+1/2', 'y+1/2,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x,-z+1/2', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', '-x,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x+1/2,-z+1/2'], 'universal_h_m': 'I4/m(a+b,-a+b,c)'}, {'hall': '-P 4 (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P4/m', 'hermann_mauguin_u': 'P4/m', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z'], 'number': 83, 'point_group': '4/m', 'schoenflies': 'C4h^1', 'short_h_m': 'P4/m', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z'], 'universal_h_m': 'P4/m(a+b,-a+b,c)'}, {'hall': '-I 4 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x,-z', 'x,y,-z', '-y,x+1/2,-z', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-x,-y,-z', 'y,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-x,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x,-z+1/2'], 'universal_h_m': 'I4/m(a+b+1/2,-a+b,c)'}, {'hall': '-P 4c (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P42/m', 'hermann_mauguin_u': 'P4_2/m', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2'], 'number': 84, 'point_group': '4/m', 'schoenflies': 'C4h^2', 'short_h_m': 'P4_2/m', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z+1/2'], 'universal_h_m': 'P42/m(a+b,-a+b,c)'}, {'hall': '-I 4 (x+1/2,y,z)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', '-x,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y,-z', '-y+1/2,x+1/2,-z', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z+1/2'], 'universal_h_m': 'I4/m(a+1/2,b,c)'}, {'hall': '-I 4 (x+1/2,y,z+1/4)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', '-x,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z'], 'universal_h_m': 'I4/m(a+1/2,b,c-1/4)'}, {'hall': '-P 4 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P4/m', 'hermann_mauguin_u': 'P4/m', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z'], 'number': 83, 'point_group': '4/m', 'schoenflies': 'C4h^1', 'short_h_m': 'P4/m', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y,-z', '-y+1/2,x,-z', 'x+1/2,y+1/2,z', '-y,x+1/2,z', '-x,-y,z', 'y+1/2,-x,z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z'], 'universal_h_m': 'P4/m(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 (x+1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x,-z+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y,z+1/2', 'y+1/2,-x,z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z'], 'universal_h_m': 'I4/m(a-1/4,b-1/4,c+1/4)'}, {'hall': '-I 4 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z+1/4)', 'hermann_mauguin': 'I4/m', 'hermann_mauguin_u': 'I4/m', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z'], 'number': 87, 'point_group': '4/m', 'schoenflies': 'C4h^5', 'short_h_m': 'I4/m', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x,-z+1/2', 'x,y,-z+1/2', '-y,x+1/2,-z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-x,-y,-z+1/2', 'y,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x,-z+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-x,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y,-z', '-y+1/2,x+1/2,-z', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y+1/2,-z', '-y,x,-z'], 'universal_h_m': 'I4/m(a+b+1/2,-a+b,c-1/4)'}, {'hall': '-P 4c (1/2*x+1/2*y,-1/2*x+1/2*y,z+1/4)', 'hermann_mauguin': 'P42/m', 'hermann_mauguin_u': 'P4_2/m', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z'], 'number': 84, 'point_group': '4/m', 'schoenflies': 'C4h^2', 'short_h_m': 'P4_2/m', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-x,-y,-z+1/2', 'y,-x,-z', 'x,y,-z+1/2', '-y,x,-z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z'], 'universal_h_m': 'P42/m(a+b,-a+b,c-1/4)'}, {'hall': '-P 4c (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P42/m', 'hermann_mauguin_u': 'P4_2/m', 'ncsym': ['x,y,z', '-y,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z+1/2', '-x,-y,-z', 'y,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z+1/2'], 'number': 84, 'point_group': '4/m', 'schoenflies': 'C4h^2', 'short_h_m': 'P4_2/m', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z+1/2', 'x,y,-z', '-y+1/2,x,-z+1/2', 'x+1/2,y+1/2,z', '-y,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x,z+1/2', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2'], 'universal_h_m': 'P42/m(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'y,x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', '-y+1/2,-x,-z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z+1/2', 'y+1/2,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x,-z+1/2', 'y+1/2,x,z+1/2', '-x+1/2,y,z+1/2', '-y+1/2,-x,z+1/2', 'x+1/2,-y,z+1/2', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x+1/2,-z+1/2', 'y,x+1/2,z+1/2', '-x,y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'I4/mmm(a+b,-a+b,c)'}, {'hall': '-P 4 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P4/mmm', 'hermann_mauguin_u': 'P4/mmm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'y,x,z'], 'number': 123, 'point_group': '4/mmm', 'schoenflies': 'D4h^1', 'short_h_m': 'P4/mmm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'y,x,z', '-x,y,z', '-y,-x,z', 'x,-y,z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P4/mmm(a+b,-a+b,c)'}, {'hall': '-I 4 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z+1/2', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'y,x,z+1/2', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', '-y+1/2,-x,-z', 'x+1/2,-y,-z', 'y+1/2,x,-z', '-x+1/2,y,-z', '-x+1/2,-y,-z+1/2', 'y+1/2,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x,-z+1/2', 'y+1/2,x,z', '-x+1/2,y,z', '-y+1/2,-x,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', '-y,-x+1/2,-z', 'x,-y+1/2,-z', 'y,x+1/2,-z', '-x,y+1/2,-z', '-x,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x+1/2,-z+1/2', 'y,x+1/2,z', '-x,y+1/2,z', '-y,-x+1/2,z', 'x,-y+1/2,z'], 'universal_h_m': 'I4/mcm(a+b,-a+b,c)'}, {'hall': '-P 4 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P4/mcc', 'hermann_mauguin_u': 'P4/mcc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2'], 'number': 124, 'point_group': '4/mmm', 'schoenflies': 'D4h^2', 'short_h_m': 'P4/mcc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z+1/2', 'x,-y,-z+1/2', 'y,x,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'y,-x,-z', 'x,y,-z', '-y,x,-z', 'y,x,z+1/2', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P4/mcc(a+b,-a+b,c)'}, {'hall': '-I 4 2c (x,y,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x,-y,-z+1/2', 'y,-x,-z+1/2', 'x,y,-z+1/2', '-y,x,-z+1/2', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'y,x,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'I4/mcm(a,b,c+1/4)'}, {'hall': '-I 4 2 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z', 'y+1/2,x+1/2,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-y,-x,-z', 'x,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x,-z', 'x,y,-z', '-y,x+1/2,-z', 'y+1/2,x+1/2,z', '-x+1/2,y,z', '-y,-x,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y,-z', 'y,x,-z', '-x,y+1/2,-z', '-x,-y,-z', 'y,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z', 'y,x,z', '-x,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y,z', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-y+1/2,-x,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'y,x+1/2,z+1/2', '-x,y,z+1/2', '-y+1/2,-x,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x,-z+1/2', 'y+1/2,x,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'I4/mmm(a+b+1/2,-a+b,c)'}, {'hall': '-P 4 2 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P4/mmm', 'hermann_mauguin_u': 'P4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z', 'y+1/2,x+1/2,z'], 'number': 123, 'point_group': '4/mmm', 'schoenflies': 'D4h^1', 'short_h_m': 'P4/mmm', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y,-z', '-y+1/2,x,-z', 'y,x,z', '-x+1/2,y,z', '-y+1/2,-x+1/2,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-y,x+1/2,z', '-x,-y,z', 'y+1/2,-x,z', '-y,-x,-z', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', 'y+1/2,x+1/2,z', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z'], 'universal_h_m': 'P4/mmm(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 2c (x+1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z', 'y+1/2,x+1/2,z'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z', 'y,x,-z', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x,-z+1/2', '-x+1/2,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'y,x,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z', 'y+1/2,x+1/2,z'], 'universal_h_m': 'I4/mcm(a-1/4,b-1/4,c+1/4)'}, {'hall': '-I 4 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-x,-y,-z+1/2', 'y,-x,-z+1/2', 'x,y,-z+1/2', '-y,x,-z+1/2', 'y,x,z+1/2', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', '-y+1/2,-x,-z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y,-z', '-y+1/2,x,-z', 'y+1/2,x,z', '-x+1/2,y,z', '-y+1/2,-x,z', 'x+1/2,-y,z', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y+1/2,-z', '-y,x+1/2,-z', 'y,x+1/2,z', '-x,y+1/2,z', '-y,-x+1/2,z', 'x,-y+1/2,z'], 'universal_h_m': 'I4/mcm(a+b,-a+b,c+1/4)'}, {'hall': '-P 4 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z-1/4)', 'hermann_mauguin': 'P4/mcc', 'hermann_mauguin_u': 'P4/mcc', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 124, 'point_group': '4/mmm', 'schoenflies': 'D4h^2', 'short_h_m': 'P4/mcc', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-y,-x,-z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-x,-y,-z+1/2', 'y,-x,-z+1/2', 'x,y,-z+1/2', '-y,x,-z+1/2', 'y,x,z+1/2', '-x,y,z+1/2', '-y,-x,z+1/2', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P4/mcc(a+b,-a+b,c+1/4)'}, {'hall': '-I 4 2c (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-y,-x,-z+1/2', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x,-z', 'x,y,-z', '-y,x+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y,z+1/2', '-y,-x,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y,-z+1/2', 'y,x,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'y,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z', 'y,x,z+1/2', '-x,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-y+1/2,-x,-z', 'x+1/2,-y+1/2,-z', 'y,x+1/2,-z', '-x,y,-z', '-x,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', 'y,x+1/2,z', '-x,y,z', '-y+1/2,-x,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-y,-x+1/2,-z', 'x,-y,-z', 'y+1/2,x,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y+1/2,-z+1/2', '-y,x,-z+1/2', 'y+1/2,x,z', '-x+1/2,y+1/2,z', '-y,-x+1/2,z', 'x,-y,z'], 'universal_h_m': 'I4/mcm(a+b+1/2,-a+b,c)'}, {'hall': '-P 4 2c (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P4/mcc', 'hermann_mauguin_u': 'P4/mcc', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 124, 'point_group': '4/mmm', 'schoenflies': 'D4h^2', 'short_h_m': 'P4/mcc', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y,-z', '-y+1/2,x,-z', 'y,x,z+1/2', '-x+1/2,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-y,x+1/2,z', '-x,-y,z', 'y+1/2,-x,z', '-y,-x,-z+1/2', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P4/mcc(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 2 (x+1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x,-z+1/2', '-x+1/2,y,z', '-y+1/2,-x+1/2,z', 'x,-y+1/2,z', 'y,x,z', 'x+1/2,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z', '-y,-x,-z', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'I4/mmm(a-1/4,b-1/4,c+1/4)'}, {'hall': '-I 4 2 (x+1/2,y,z+1/4)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z', '-y+1/2,-x+1/2,z', 'x,-y,z', 'y+1/2,x+1/2,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x,y,z', '-y+1/2,-x+1/2,z', 'x,-y,z', 'y+1/2,x+1/2,z', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y,x,z+1/2'], 'universal_h_m': 'I4/mmm(a+1/2,b,c-1/4)'}, {'hall': '-I 4 2c (x+1/2,y,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x,-y,-z', 'y+1/2,x+1/2,-z', '-x,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z+1/2', 'y+1/2,x+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y+1/2,-z', '-y,x,-z', '-x+1/2,y+1/2,z', '-y,-x,z', 'x+1/2,-y+1/2,z', 'y,x,z'], 'universal_h_m': 'I4/mcm(a+1/2,b,c+1/4)'}, {'hall': '-P 4c 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P42/mcm', 'hermann_mauguin_u': 'P4_2/mcm', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'y,x,z+1/2'], 'number': 132, 'point_group': '4/mmm', 'schoenflies': 'D4h^10', 'short_h_m': 'P4_2/mcm', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-y,-x,-z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', 'y,x,z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P42/mcm(a+b,-a+b,c)'}, {'hall': '-I 4 2 (x+1/2,y,z)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-y,-x,-z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'y,x,z+1/2'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x,-y,-z', 'y+1/2,x+1/2,-z', '-x,y,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y,-z', '-y+1/2,x+1/2,-z', '-x,y,z', '-y+1/2,-x+1/2,z', 'x,-y,z', 'y+1/2,x+1/2,z', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y,x,z+1/2'], 'universal_h_m': 'I4/mmm(a+1/2,b,c)'}, {'hall': '-P 4c 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z)', 'hermann_mauguin': 'P42/mmc', 'hermann_mauguin_u': 'P4_2/mmc', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'y,x,z'], 'number': 131, 'point_group': '4/mmm', 'schoenflies': 'D4h^9', 'short_h_m': 'P4_2/mmc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-y,-x,-z', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', 'y,x,z', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z', '-y+1/2,x+1/2,-z+1/2', 'y+1/2,x+1/2,z', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P42/mmc(a+b,-a+b,c)'}, {'hall': '-I 4 2c (x+1/2,y,z)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-y,-x,-z', '-x,-y,-z', 'y,-x,-z+1/2', 'x,y,-z', '-y,x,-z+1/2', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'y,x,z'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y+1/2,x+1/2,z', '-x,-y,z', 'y+1/2,-x+1/2,z', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y,-z', '-y+1/2,x+1/2,-z', '-x,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z+1/2', 'y+1/2,x+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y+1/2,z+1/2', 'y,-x,z+1/2', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z+1/2', '-x+1/2,y+1/2,z', '-y,-x,z', 'x+1/2,-y+1/2,z', 'y,x,z'], 'universal_h_m': 'I4/mcm(a+1/2,b,c)'}, {'hall': '-I 4 2c (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z', 'y,x,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-y,-x,-z', 'x,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x,-z+1/2', 'x,y,-z+1/2', '-y,x+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y,z+1/2', '-y,-x,z+1/2', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z', 'x+1/2,-y,-z', 'y,x,-z', '-x,y+1/2,-z', '-x,-y,-z+1/2', 'y,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x,-z+1/2', 'y,x,z+1/2', '-x,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y,z+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-y+1/2,-x,-z+1/2', 'x+1/2,-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x,y,-z+1/2', '-x,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y,-z', '-y+1/2,x+1/2,-z', 'y,x+1/2,z', '-x,y,z', '-y+1/2,-x,z', 'x+1/2,-y+1/2,z', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x,-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y+1/2,-z', '-y,x,-z', 'y+1/2,x,z', '-x+1/2,y+1/2,z', '-y,-x+1/2,z', 'x,-y,z'], 'universal_h_m': 'I4/mcm(a+b+1/2,-a+b,c+1/4)'}, {'hall': '-P 4c 2c (1/2*x+1/2*y,-1/2*x+1/2*y,z-1/4)', 'hermann_mauguin': 'P42/mcm', 'hermann_mauguin_u': 'P4_2/mcm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z', 'y,x,z+1/2'], 'number': 132, 'point_group': '4/mmm', 'schoenflies': 'D4h^10', 'short_h_m': 'P4_2/mcm', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-y,-x,-z', 'x,-y,-z+1/2', 'y,x,-z', '-x,y,-z+1/2', '-x,-y,-z+1/2', 'y,-x,-z', 'x,y,-z+1/2', '-y,x,-z', 'y,x,z+1/2', '-x,y,z', '-y,-x,z+1/2', 'x,-y,z', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z', 'x+1/2,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z', '-x+1/2,y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z'], 'universal_h_m': 'P42/mcm(a+b,-a+b,c+1/4)'}, {'hall': '-P 4c 2c (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P42/mcm', 'hermann_mauguin_u': 'P4_2/mcm', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', '-x,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y,z', 'y+1/2,x+1/2,z+1/2'], 'number': 132, 'point_group': '4/mmm', 'schoenflies': 'D4h^10', 'short_h_m': 'P4_2/mcm', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'x,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y,-z', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z+1/2', 'x,y,-z', '-y+1/2,x,-z+1/2', 'y,x,z+1/2', '-x+1/2,y,z', '-y+1/2,-x+1/2,z+1/2', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-y,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x,z+1/2', '-y,-x,-z+1/2', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y,z'], 'universal_h_m': 'P42/mcm(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 2c (x-1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'I4/mcm', 'hermann_mauguin_u': 'I4/mcm', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z', 'y,x,-z+1/2', '-x+1/2,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', '-x,y+1/2,z', '-y,-x,z+1/2', 'x+1/2,-y,z', 'y+1/2,x+1/2,z+1/2'], 'number': 140, 'point_group': '4/mmm', 'schoenflies': 'D4h^18', 'short_h_m': 'I4/mcm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', 'x,-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+1/2,y,-z', '-y,-x,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x,-z+1/2', 'x,y,-z+1/2', '-y,x+1/2,-z+1/2', '-x+1/2,y,z+1/2', '-y,-x,z+1/2', 'x,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x,z+1/2', '-x,-y,z+1/2', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z+1/2', 'y,x,-z+1/2', '-x,y+1/2,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', '-x,-y,-z', 'y,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z', '-x,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y,z', 'y,x,z'], 'universal_h_m': 'I4/mcm(a+1/4,b-1/4,c+1/4)'}, {'hall': '-I 4 2 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y+1/4,z+1/4)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', '-y,-x,-z+1/2', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x,-z+1/2', 'x,y,-z+1/2', '-y,x+1/2,-z+1/2', 'y+1/2,x+1/2,z', '-x+1/2,y,z', '-y,-x,z', 'x,-y+1/2,z', 'x+1/2,y+1/2,z', '-y+1/2,x,z', '-x,-y,z', 'y,-x+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y,-z+1/2', 'y,x,-z+1/2', '-x,y+1/2,-z+1/2', '-x,-y,-z+1/2', 'y,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x,-z+1/2', 'y,x,z', '-x,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y,z', 'x+1/2,y,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x,z+1/2', '-y+1/2,-x,-z', 'x+1/2,-y+1/2,-z', 'y,x+1/2,-z', '-x,y,-z', '-x,-y+1/2,-z', 'y,-x,-z', 'x+1/2,y,-z', '-y+1/2,x+1/2,-z', 'y,x+1/2,z+1/2', '-x,y,z+1/2', '-y+1/2,-x,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y+1/2,z+1/2', '-y,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x+1/2,z+1/2', '-y,-x+1/2,-z', 'x,-y,-z', 'y+1/2,x,-z', '-x+1/2,y+1/2,-z', '-x+1/2,-y,-z', 'y+1/2,-x+1/2,-z', 'x,y+1/2,-z', '-y,x,-z', 'y+1/2,x,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x,-y,z+1/2'], 'universal_h_m': 'I4/mmm(a+b+1/2,-a+b,c-1/4)'}, {'hall': '-P 4c 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z+1/4)', 'hermann_mauguin': 'P42/mmc', 'hermann_mauguin_u': 'P4_2/mmc', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z'], 'number': 131, 'point_group': '4/mmm', 'schoenflies': 'D4h^9', 'short_h_m': 'P4_2/mmc', 'symops': ['x,y,z', '-y,x,z+1/2', '-x,-y,z', 'y,-x,z+1/2', '-y,-x,-z+1/2', 'x,-y,-z', 'y,x,-z+1/2', '-x,y,-z', '-x,-y,-z+1/2', 'y,-x,-z', 'x,y,-z+1/2', '-y,x,-z', 'y,x,z', '-x,y,z+1/2', '-y,-x,z', 'x,-y,z+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'x+1/2,-y+1/2,-z', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,-z', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z', 'y+1/2,x+1/2,z', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z+1/2'], 'universal_h_m': 'P42/mmc(a+b,-a+b,c-1/4)'}, {'hall': '-P 4c 2 (1/2*x+1/2*y-1/4,-1/2*x+1/2*y-1/4,z)', 'hermann_mauguin': 'P42/mmc', 'hermann_mauguin_u': 'P4_2/mmc', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z'], 'number': 131, 'point_group': '4/mmm', 'schoenflies': 'D4h^9', 'short_h_m': 'P4_2/mmc', 'symops': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', '-y+1/2,-x+1/2,-z', 'x,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y,-z+1/2', '-x+1/2,-y+1/2,-z', 'y,-x+1/2,-z+1/2', 'x,y,-z', '-y+1/2,x,-z+1/2', 'y,x,z', '-x+1/2,y,z+1/2', '-y+1/2,-x+1/2,z', 'x,-y+1/2,z+1/2', 'x+1/2,y+1/2,z', '-y,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x,z+1/2', '-y,-x,-z', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', 'y+1/2,x+1/2,z', '-x,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y,z+1/2'], 'universal_h_m': 'P42/mmc(a+b,-a+b+1/2,c)'}, {'hall': '-I 4 2 (x-1/4,y+1/4,z-1/4)', 'hermann_mauguin': 'I4/mmm', 'hermann_mauguin_u': 'I4/mmm', 'ncsym': ['x,y,z', '-y+1/2,x,z+1/2', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z+1/2', 'x,-y+1/2,-z+1/2', 'y,x,-z', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z+1/2', '-x,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z'], 'number': 139, 'point_group': '4/mmm', 'schoenflies': 'D4h^17', 'short_h_m': 'I4/mmm', 'symops': ['x,y,z', '-y,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x,z', 'x,-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-y,-x,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x,-z+1/2', 'x,y,-z+1/2', '-y,x+1/2,-z+1/2', '-x+1/2,y,z', '-y,-x,z', 'x,-y+1/2,z', 'y+1/2,x+1/2,z', 'x+1/2,y+1/2,z+1/2', '-y+1/2,x,z+1/2', '-x,-y,z+1/2', 'y,-x+1/2,z+1/2', 'x+1/2,-y,-z', 'y,x,-z', '-x,y+1/2,-z', '-y+1/2,-x+1/2,-z', '-x,-y,-z', 'y,-x+1/2,-z', 'x+1/2,y+1/2,-z', '-y+1/2,x,-z', '-x,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y,z+1/2', 'y,x,z+1/2'], 'universal_h_m': 'I4/mmm(a+1/4,b-1/4,c+1/4)'}, {'hall': '-P 6 (1/2*x,1/2*y,1/2*z)', 'hermann_mauguin': 'P6/m', 'hermann_mauguin_u': 'P6/m', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z'], 'number': 175, 'point_group': '6/m', 'schoenflies': 'C6h^1', 'short_h_m': 'P6/m', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'x+1/2,y,z', 'x-y+1/2,x,z', '-y+1/2,x-y,z', '-x+1/2,-y,z', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z', 'y+1/2,-x+y,-z', 'x+1/2,y,-z', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z', 'x,y+1/2,z', 'x-y,x+1/2,z', '-y,x-y+1/2,z', '-x,-y+1/2,z', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z', 'y,-x+y+1/2,-z', 'x,y+1/2,-z', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z', 'x,y,z+1/2', 'x-y,x,z+1/2', '-y,x-y,z+1/2', '-x,-y,z+1/2', '-x+y,-x,z+1/2', 'y,-x+y,z+1/2', '-x,-y,-z+1/2', '-x+y,-x,-z+1/2', 'y,-x+y,-z+1/2', 'x,y,-z+1/2', 'x-y,x,-z+1/2', '-y,x-y,-z+1/2', 'x+1/2,y,z+1/2', 'x-y+1/2,x,z+1/2', '-y+1/2,x-y,z+1/2', '-x+1/2,-y,z+1/2', '-x+y+1/2,-x,z+1/2', 'y+1/2,-x+y,z+1/2', '-x+1/2,-y,-z+1/2', '-x+y+1/2,-x,-z+1/2', 'y+1/2,-x+y,-z+1/2', 'x+1/2,y,-z+1/2', 'x-y+1/2,x,-z+1/2', '-y+1/2,x-y,-z+1/2', 'x,y+1/2,z+1/2', 'x-y,x+1/2,z+1/2', '-y,x-y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x+y,-x+1/2,z+1/2', 'y,-x+y+1/2,z+1/2', '-x,-y+1/2,-z+1/2', '-x+y,-x+1/2,-z+1/2', 'y,-x+y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', 'x-y,x+1/2,-z+1/2', '-y,x-y+1/2,-z+1/2', 'x+1/2,y+1/2,z+1/2', 'x-y+1/2,x+1/2,z+1/2', '-y+1/2,x-y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+y+1/2,-x+1/2,z+1/2', 'y+1/2,-x+y+1/2,z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+y+1/2,-x+1/2,-z+1/2', 'y+1/2,-x+y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x-y+1/2,x+1/2,-z+1/2', '-y+1/2,x-y+1/2,-z+1/2'], 'universal_h_m': 'P6/m(2*a,2*b,2*c)'}, {'hall': '-P 6 (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P6/m', 'hermann_mauguin_u': 'P6/m', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z'], 'number': 175, 'point_group': '6/m', 'schoenflies': 'C6h^1', 'short_h_m': 'P6/m', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'x+1/2,y,z', 'x-y+1/2,x,z', '-y+1/2,x-y,z', '-x+1/2,-y,z', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z', 'y+1/2,-x+y,-z', 'x+1/2,y,-z', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z', 'x,y+1/2,z', 'x-y,x+1/2,z', '-y,x-y+1/2,z', '-x,-y+1/2,z', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z', 'y,-x+y+1/2,-z', 'x,y+1/2,-z', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z'], 'universal_h_m': 'P6/m(2*a,2*b,c)'}, {'hall': '-P 6c (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P63/m', 'hermann_mauguin_u': 'P6_3/m', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2'], 'number': 176, 'point_group': '6/m', 'schoenflies': 'C6h^2', 'short_h_m': 'P6_3/m', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2', 'x+1/2,y,z', 'x-y+1/2,x,z+1/2', '-y+1/2,x-y,z', '-x+1/2,-y,z+1/2', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z+1/2', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z+1/2', 'y+1/2,-x+y,-z', 'x+1/2,y,-z+1/2', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z+1/2', 'x,y+1/2,z', 'x-y,x+1/2,z+1/2', '-y,x-y+1/2,z', '-x,-y+1/2,z+1/2', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z+1/2', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z+1/2', 'y,-x+y+1/2,-z', 'x,y+1/2,-z+1/2', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z+1/2', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z+1/2', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z+1/2', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z+1/2', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z+1/2', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z+1/2'], 'universal_h_m': 'P63/m(2*a,2*b,c)'}, {'hall': '-P 6 2 (1/2*x,1/2*y,1/2*z)', 'hermann_mauguin': 'P6/mmm', 'hermann_mauguin_u': 'P6/mmm', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'number': 191, 'point_group': '6/mmm', 'schoenflies': 'D6h^1', 'short_h_m': 'P6/mmm', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z', 'x+1/2,y,z', 'x-y+1/2,x,z', '-y+1/2,x-y,z', '-x+1/2,-y,z', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z', '-y+1/2,-x,-z', 'x-y+1/2,-y,-z', 'x+1/2,x-y,-z', 'y+1/2,x,-z', '-x+y+1/2,y,-z', '-x+1/2,-x+y,-z', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z', 'y+1/2,-x+y,-z', 'x+1/2,y,-z', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z', 'y+1/2,x,z', '-x+y+1/2,y,z', '-x+1/2,-x+y,z', '-y+1/2,-x,z', 'x-y+1/2,-y,z', 'x+1/2,x-y,z', 'x,y+1/2,z', 'x-y,x+1/2,z', '-y,x-y+1/2,z', '-x,-y+1/2,z', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z', '-y,-x+1/2,-z', 'x-y,-y+1/2,-z', 'x,x-y+1/2,-z', 'y,x+1/2,-z', '-x+y,y+1/2,-z', '-x,-x+y+1/2,-z', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z', 'y,-x+y+1/2,-z', 'x,y+1/2,-z', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z', 'y,x+1/2,z', '-x+y,y+1/2,z', '-x,-x+y+1/2,z', '-y,-x+1/2,z', 'x-y,-y+1/2,z', 'x,x-y+1/2,z', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,-z', 'x-y+1/2,-y+1/2,-z', 'x+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+y+1/2,y+1/2,-z', '-x+1/2,-x+y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,z', '-x+y+1/2,y+1/2,z', '-x+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,z', 'x-y+1/2,-y+1/2,z', 'x+1/2,x-y+1/2,z', 'x,y,z+1/2', 'x-y,x,z+1/2', '-y,x-y,z+1/2', '-x,-y,z+1/2', '-x+y,-x,z+1/2', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z+1/2', 'x,x-y,-z+1/2', 'y,x,-z+1/2', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/2', '-x,-y,-z+1/2', '-x+y,-x,-z+1/2', 'y,-x+y,-z+1/2', 'x,y,-z+1/2', 'x-y,x,-z+1/2', '-y,x-y,-z+1/2', 'y,x,z+1/2', '-x+y,y,z+1/2', '-x,-x+y,z+1/2', '-y,-x,z+1/2', 'x-y,-y,z+1/2', 'x,x-y,z+1/2', 'x+1/2,y,z+1/2', 'x-y+1/2,x,z+1/2', '-y+1/2,x-y,z+1/2', '-x+1/2,-y,z+1/2', '-x+y+1/2,-x,z+1/2', 'y+1/2,-x+y,z+1/2', '-y+1/2,-x,-z+1/2', 'x-y+1/2,-y,-z+1/2', 'x+1/2,x-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+y+1/2,y,-z+1/2', '-x+1/2,-x+y,-z+1/2', '-x+1/2,-y,-z+1/2', '-x+y+1/2,-x,-z+1/2', 'y+1/2,-x+y,-z+1/2', 'x+1/2,y,-z+1/2', 'x-y+1/2,x,-z+1/2', '-y+1/2,x-y,-z+1/2', 'y+1/2,x,z+1/2', '-x+y+1/2,y,z+1/2', '-x+1/2,-x+y,z+1/2', '-y+1/2,-x,z+1/2', 'x-y+1/2,-y,z+1/2', 'x+1/2,x-y,z+1/2', 'x,y+1/2,z+1/2', 'x-y,x+1/2,z+1/2', '-y,x-y+1/2,z+1/2', '-x,-y+1/2,z+1/2', '-x+y,-x+1/2,z+1/2', 'y,-x+y+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x-y,-y+1/2,-z+1/2', 'x,x-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x+y,y+1/2,-z+1/2', '-x,-x+y+1/2,-z+1/2', '-x,-y+1/2,-z+1/2', '-x+y,-x+1/2,-z+1/2', 'y,-x+y+1/2,-z+1/2', 'x,y+1/2,-z+1/2', 'x-y,x+1/2,-z+1/2', '-y,x-y+1/2,-z+1/2', 'y,x+1/2,z+1/2', '-x+y,y+1/2,z+1/2', '-x,-x+y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x-y,-y+1/2,z+1/2', 'x,x-y+1/2,z+1/2', 'x+1/2,y+1/2,z+1/2', 'x-y+1/2,x+1/2,z+1/2', '-y+1/2,x-y+1/2,z+1/2', '-x+1/2,-y+1/2,z+1/2', '-x+y+1/2,-x+1/2,z+1/2', 'y+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'x-y+1/2,-y+1/2,-z+1/2', 'x+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+y+1/2,y+1/2,-z+1/2', '-x+1/2,-x+y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z+1/2', '-x+y+1/2,-x+1/2,-z+1/2', 'y+1/2,-x+y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x-y+1/2,x+1/2,-z+1/2', '-y+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+y+1/2,y+1/2,z+1/2', '-x+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x-y+1/2,-y+1/2,z+1/2', 'x+1/2,x-y+1/2,z+1/2'], 'universal_h_m': 'P6/mmm(2*a,2*b,2*c)'}, {'hall': '-P 6 2 (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P6/mmm', 'hermann_mauguin_u': 'P6/mmm', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z'], 'number': 191, 'point_group': '6/mmm', 'schoenflies': 'D6h^1', 'short_h_m': 'P6/mmm', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z', 'x-y,-y,-z', 'x,x-y,-z', 'y,x,-z', '-x+y,y,-z', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z', '-x+y,y,z', '-x,-x+y,z', '-y,-x,z', 'x-y,-y,z', 'x,x-y,z', 'x+1/2,y,z', 'x-y+1/2,x,z', '-y+1/2,x-y,z', '-x+1/2,-y,z', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z', '-y+1/2,-x,-z', 'x-y+1/2,-y,-z', 'x+1/2,x-y,-z', 'y+1/2,x,-z', '-x+y+1/2,y,-z', '-x+1/2,-x+y,-z', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z', 'y+1/2,-x+y,-z', 'x+1/2,y,-z', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z', 'y+1/2,x,z', '-x+y+1/2,y,z', '-x+1/2,-x+y,z', '-y+1/2,-x,z', 'x-y+1/2,-y,z', 'x+1/2,x-y,z', 'x,y+1/2,z', 'x-y,x+1/2,z', '-y,x-y+1/2,z', '-x,-y+1/2,z', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z', '-y,-x+1/2,-z', 'x-y,-y+1/2,-z', 'x,x-y+1/2,-z', 'y,x+1/2,-z', '-x+y,y+1/2,-z', '-x,-x+y+1/2,-z', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z', 'y,-x+y+1/2,-z', 'x,y+1/2,-z', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z', 'y,x+1/2,z', '-x+y,y+1/2,z', '-x,-x+y+1/2,z', '-y,-x+1/2,z', 'x-y,-y+1/2,z', 'x,x-y+1/2,z', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,-z', 'x-y+1/2,-y+1/2,-z', 'x+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,-z', '-x+y+1/2,y+1/2,-z', '-x+1/2,-x+y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,z', '-x+y+1/2,y+1/2,z', '-x+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,z', 'x-y+1/2,-y+1/2,z', 'x+1/2,x-y+1/2,z'], 'universal_h_m': 'P6/mmm(2*a,2*b,c)'}, {'hall': '-P 6 2c (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P6/mcc', 'hermann_mauguin_u': 'P6/mcc', 'ncsym': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z+1/2', 'x-y,-y,-z+1/2', 'x,x-y,-z+1/2', 'y,x,-z+1/2', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z+1/2', '-x+y,y,z+1/2', '-x,-x+y,z+1/2', '-y,-x,z+1/2', 'x-y,-y,z+1/2', 'x,x-y,z+1/2'], 'number': 192, 'point_group': '6/mmm', 'schoenflies': 'D6h^2', 'short_h_m': 'P6/mcc', 'symops': ['x,y,z', 'x-y,x,z', '-y,x-y,z', '-x,-y,z', '-x+y,-x,z', 'y,-x+y,z', '-y,-x,-z+1/2', 'x-y,-y,-z+1/2', 'x,x-y,-z+1/2', 'y,x,-z+1/2', '-x+y,y,-z+1/2', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z', 'y,-x+y,-z', 'x,y,-z', 'x-y,x,-z', '-y,x-y,-z', 'y,x,z+1/2', '-x+y,y,z+1/2', '-x,-x+y,z+1/2', '-y,-x,z+1/2', 'x-y,-y,z+1/2', 'x,x-y,z+1/2', 'x+1/2,y,z', 'x-y+1/2,x,z', '-y+1/2,x-y,z', '-x+1/2,-y,z', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z', '-y+1/2,-x,-z+1/2', 'x-y+1/2,-y,-z+1/2', 'x+1/2,x-y,-z+1/2', 'y+1/2,x,-z+1/2', '-x+y+1/2,y,-z+1/2', '-x+1/2,-x+y,-z+1/2', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z', 'y+1/2,-x+y,-z', 'x+1/2,y,-z', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z', 'y+1/2,x,z+1/2', '-x+y+1/2,y,z+1/2', '-x+1/2,-x+y,z+1/2', '-y+1/2,-x,z+1/2', 'x-y+1/2,-y,z+1/2', 'x+1/2,x-y,z+1/2', 'x,y+1/2,z', 'x-y,x+1/2,z', '-y,x-y+1/2,z', '-x,-y+1/2,z', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z', '-y,-x+1/2,-z+1/2', 'x-y,-y+1/2,-z+1/2', 'x,x-y+1/2,-z+1/2', 'y,x+1/2,-z+1/2', '-x+y,y+1/2,-z+1/2', '-x,-x+y+1/2,-z+1/2', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z', 'y,-x+y+1/2,-z', 'x,y+1/2,-z', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z', 'y,x+1/2,z+1/2', '-x+y,y+1/2,z+1/2', '-x,-x+y+1/2,z+1/2', '-y,-x+1/2,z+1/2', 'x-y,-y+1/2,z+1/2', 'x,x-y+1/2,z+1/2', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,-z+1/2', 'x-y+1/2,-y+1/2,-z+1/2', 'x+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x+y+1/2,y+1/2,-z+1/2', '-x+1/2,-x+y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,z+1/2', '-x+y+1/2,y+1/2,z+1/2', '-x+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x-y+1/2,-y+1/2,z+1/2', 'x+1/2,x-y+1/2,z+1/2'], 'universal_h_m': 'P6/mcc(2*a,2*b,c)'}, {'hall': '-P 6c 2 (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P63/mcm', 'hermann_mauguin_u': 'P6_3/mcm', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z', 'x-y,-y,-z+1/2', 'x,x-y,-z', 'y,x,-z+1/2', '-x+y,y,-z', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2', 'y,x,z', '-x+y,y,z+1/2', '-x,-x+y,z', '-y,-x,z+1/2', 'x-y,-y,z', 'x,x-y,z+1/2'], 'number': 193, 'point_group': '6/mmm', 'schoenflies': 'D6h^3', 'short_h_m': 'P6_3/mcm', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z', 'x-y,-y,-z+1/2', 'x,x-y,-z', 'y,x,-z+1/2', '-x+y,y,-z', '-x,-x+y,-z+1/2', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2', 'y,x,z', '-x+y,y,z+1/2', '-x,-x+y,z', '-y,-x,z+1/2', 'x-y,-y,z', 'x,x-y,z+1/2', 'x+1/2,y,z', 'x-y+1/2,x,z+1/2', '-y+1/2,x-y,z', '-x+1/2,-y,z+1/2', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z+1/2', '-y+1/2,-x,-z', 'x-y+1/2,-y,-z+1/2', 'x+1/2,x-y,-z', 'y+1/2,x,-z+1/2', '-x+y+1/2,y,-z', '-x+1/2,-x+y,-z+1/2', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z+1/2', 'y+1/2,-x+y,-z', 'x+1/2,y,-z+1/2', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z+1/2', 'y+1/2,x,z', '-x+y+1/2,y,z+1/2', '-x+1/2,-x+y,z', '-y+1/2,-x,z+1/2', 'x-y+1/2,-y,z', 'x+1/2,x-y,z+1/2', 'x,y+1/2,z', 'x-y,x+1/2,z+1/2', '-y,x-y+1/2,z', '-x,-y+1/2,z+1/2', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z+1/2', '-y,-x+1/2,-z', 'x-y,-y+1/2,-z+1/2', 'x,x-y+1/2,-z', 'y,x+1/2,-z+1/2', '-x+y,y+1/2,-z', '-x,-x+y+1/2,-z+1/2', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z+1/2', 'y,-x+y+1/2,-z', 'x,y+1/2,-z+1/2', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z+1/2', 'y,x+1/2,z', '-x+y,y+1/2,z+1/2', '-x,-x+y+1/2,z', '-y,-x+1/2,z+1/2', 'x-y,-y+1/2,z', 'x,x-y+1/2,z+1/2', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z+1/2', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,-z', 'x-y+1/2,-y+1/2,-z+1/2', 'x+1/2,x-y+1/2,-z', 'y+1/2,x+1/2,-z+1/2', '-x+y+1/2,y+1/2,-z', '-x+1/2,-x+y+1/2,-z+1/2', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z+1/2', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z+1/2', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,z', '-x+y+1/2,y+1/2,z+1/2', '-x+1/2,-x+y+1/2,z', '-y+1/2,-x+1/2,z+1/2', 'x-y+1/2,-y+1/2,z', 'x+1/2,x-y+1/2,z+1/2'], 'universal_h_m': 'P63/mcm(2*a,2*b,c)'}, {'hall': '-P 6c 2c (1/2*x,1/2*y,z)', 'hermann_mauguin': 'P63/mmc', 'hermann_mauguin_u': 'P6_3/mmc', 'ncsym': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2', 'y,x,z+1/2', '-x+y,y,z', '-x,-x+y,z+1/2', '-y,-x,z', 'x-y,-y,z+1/2', 'x,x-y,z'], 'number': 194, 'point_group': '6/mmm', 'schoenflies': 'D6h^4', 'short_h_m': 'P6_3/mmc', 'symops': ['x,y,z', 'x-y,x,z+1/2', '-y,x-y,z', '-x,-y,z+1/2', '-x+y,-x,z', 'y,-x+y,z+1/2', '-y,-x,-z+1/2', 'x-y,-y,-z', 'x,x-y,-z+1/2', 'y,x,-z', '-x+y,y,-z+1/2', '-x,-x+y,-z', '-x,-y,-z', '-x+y,-x,-z+1/2', 'y,-x+y,-z', 'x,y,-z+1/2', 'x-y,x,-z', '-y,x-y,-z+1/2', 'y,x,z+1/2', '-x+y,y,z', '-x,-x+y,z+1/2', '-y,-x,z', 'x-y,-y,z+1/2', 'x,x-y,z', 'x+1/2,y,z', 'x-y+1/2,x,z+1/2', '-y+1/2,x-y,z', '-x+1/2,-y,z+1/2', '-x+y+1/2,-x,z', 'y+1/2,-x+y,z+1/2', '-y+1/2,-x,-z+1/2', 'x-y+1/2,-y,-z', 'x+1/2,x-y,-z+1/2', 'y+1/2,x,-z', '-x+y+1/2,y,-z+1/2', '-x+1/2,-x+y,-z', '-x+1/2,-y,-z', '-x+y+1/2,-x,-z+1/2', 'y+1/2,-x+y,-z', 'x+1/2,y,-z+1/2', 'x-y+1/2,x,-z', '-y+1/2,x-y,-z+1/2', 'y+1/2,x,z+1/2', '-x+y+1/2,y,z', '-x+1/2,-x+y,z+1/2', '-y+1/2,-x,z', 'x-y+1/2,-y,z+1/2', 'x+1/2,x-y,z', 'x,y+1/2,z', 'x-y,x+1/2,z+1/2', '-y,x-y+1/2,z', '-x,-y+1/2,z+1/2', '-x+y,-x+1/2,z', 'y,-x+y+1/2,z+1/2', '-y,-x+1/2,-z+1/2', 'x-y,-y+1/2,-z', 'x,x-y+1/2,-z+1/2', 'y,x+1/2,-z', '-x+y,y+1/2,-z+1/2', '-x,-x+y+1/2,-z', '-x,-y+1/2,-z', '-x+y,-x+1/2,-z+1/2', 'y,-x+y+1/2,-z', 'x,y+1/2,-z+1/2', 'x-y,x+1/2,-z', '-y,x-y+1/2,-z+1/2', 'y,x+1/2,z+1/2', '-x+y,y+1/2,z', '-x,-x+y+1/2,z+1/2', '-y,-x+1/2,z', 'x-y,-y+1/2,z+1/2', 'x,x-y+1/2,z', 'x+1/2,y+1/2,z', 'x-y+1/2,x+1/2,z+1/2', '-y+1/2,x-y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+y+1/2,-x+1/2,z', 'y+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'x-y+1/2,-y+1/2,-z', 'x+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,-z', '-x+y+1/2,y+1/2,-z+1/2', '-x+1/2,-x+y+1/2,-z', '-x+1/2,-y+1/2,-z', '-x+y+1/2,-x+1/2,-z+1/2', 'y+1/2,-x+y+1/2,-z', 'x+1/2,y+1/2,-z+1/2', 'x-y+1/2,x+1/2,-z', '-y+1/2,x-y+1/2,-z+1/2', 'y+1/2,x+1/2,z+1/2', '-x+y+1/2,y+1/2,z', '-x+1/2,-x+y+1/2,z+1/2', '-y+1/2,-x+1/2,z', 'x-y+1/2,-y+1/2,z+1/2', 'x+1/2,x-y+1/2,z'], 'universal_h_m': 'P63/mmc(2*a,2*b,c)'}, {'hall': '-F 2 2 3 (x+1/4,y+1/4,z+1/4)', 'hermann_mauguin': 'Fm-3', 'hermann_mauguin_u': 'Fm-3', 'ncsym': ['x,y,z', '-x,-y,z', 'x,-y,-z', '-x,y,-z', 'z,x,y', '-z,-x,y', 'z,-x,-y', '-z,x,-y', 'y,z,x', 'y,-z,-x', '-y,z,-x', '-y,-z,x', '-x+1/2,-y+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2'], 'number': 202, 'point_group': 'm-3', 'schoenflies': 'Th^3', 'short_h_m': 'Fm-3', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', 'z,x,y', '-z+1/2,-x+1/2,y', 'z,-x+1/2,-y+1/2', '-z+1/2,x,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z+1/2,x', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z', '-z+1/2,-x+1/2,-y+1/2', 'z,x,-y+1/2', '-z+1/2,x,y', 'z,-x+1/2,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z,x', 'y,-z+1/2,x', 'y,z,-x+1/2', 'x,y+1/2,z+1/2', '-x+1/2,-y,z+1/2', 'x,-y,-z', '-x+1/2,y+1/2,-z', 'z,x+1/2,y+1/2', '-z+1/2,-x,y+1/2', 'z,-x,-y', '-z+1/2,x+1/2,-y', 'y,z+1/2,x+1/2', 'y,-z,-x', '-y+1/2,z+1/2,-x', '-y+1/2,-z,x+1/2', '-x+1/2,-y,-z', 'x,y+1/2,-z', '-x+1/2,y+1/2,z+1/2', 'x,-y,z+1/2', '-z+1/2,-x,-y', 'z,x+1/2,-y', '-z+1/2,x+1/2,y+1/2', 'z,-x,y+1/2', '-y+1/2,-z,-x', '-y+1/2,z+1/2,x+1/2', 'y,-z,x+1/2', 'y,z+1/2,-x', 'x+1/2,y,z+1/2', '-x,-y+1/2,z+1/2', 'x+1/2,-y+1/2,-z', '-x,y,-z', 'z+1/2,x,y+1/2', '-z,-x+1/2,y+1/2', 'z+1/2,-x+1/2,-y', '-z,x,-y', 'y+1/2,z,x+1/2', 'y+1/2,-z+1/2,-x', '-y,z,-x', '-y,-z+1/2,x+1/2', '-x,-y+1/2,-z', 'x+1/2,y,-z', '-x,y,z+1/2', 'x+1/2,-y+1/2,z+1/2', '-z,-x+1/2,-y', 'z+1/2,x,-y', '-z,x,y+1/2', 'z+1/2,-x+1/2,y+1/2', '-y,-z+1/2,-x', '-y,z,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'y+1/2,z,-x', 'x+1/2,y+1/2,z', '-x,-y,z', 'x+1/2,-y,-z+1/2', '-x,y+1/2,-z+1/2', 'z+1/2,x+1/2,y', '-z,-x,y', 'z+1/2,-x,-y+1/2', '-z,x+1/2,-y+1/2', 'y+1/2,z+1/2,x', 'y+1/2,-z,-x+1/2', '-y,z+1/2,-x+1/2', '-y,-z,x', '-x,-y,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-x,y+1/2,z', 'x+1/2,-y,z', '-z,-x,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-z,x+1/2,y', 'z+1/2,-x,y', '-y,-z,-x+1/2', '-y,z+1/2,x', 'y+1/2,-z,x', 'y+1/2,z+1/2,-x+1/2'], 'universal_h_m': 'Fm-3(a-1/4,b-1/4,c-1/4)'}, {'hall': '-I 2 2 3 (x+1/4,y+1/4,z+1/4)', 'hermann_mauguin': 'Im-3', 'hermann_mauguin_u': 'Im-3', 'ncsym': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', 'z,x,y', '-z+1/2,-x+1/2,y', 'z,-x+1/2,-y+1/2', '-z+1/2,x,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z+1/2,x', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2', '-z,-x,-y', 'z+1/2,x+1/2,-y', '-z,x+1/2,y+1/2', 'z+1/2,-x,y+1/2', '-y,-z,-x', '-y,z+1/2,x+1/2', 'y+1/2,-z,x+1/2', 'y+1/2,z+1/2,-x'], 'number': 204, 'point_group': 'm-3', 'schoenflies': 'Th^5', 'short_h_m': 'Im-3', 'symops': ['x,y,z', '-x+1/2,-y+1/2,z', 'x,-y+1/2,-z+1/2', '-x+1/2,y,-z+1/2', 'z,x,y', '-z+1/2,-x+1/2,y', 'z,-x+1/2,-y+1/2', '-z+1/2,x,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', '-y+1/2,z,-x+1/2', '-y+1/2,-z+1/2,x', '-x+1/2,-y+1/2,-z+1/2', 'x,y,-z+1/2', '-x+1/2,y,z', 'x,-y+1/2,z', '-z+1/2,-x+1/2,-y+1/2', 'z,x,-y+1/2', '-z+1/2,x,y', 'z,-x+1/2,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z,x', 'y,-z+1/2,x', 'y,z,-x+1/2', 'x+1/2,y+1/2,z+1/2', '-x,-y,z+1/2', 'x+1/2,-y,-z', '-x,y+1/2,-z', 'z+1/2,x+1/2,y+1/2', '-z,-x,y+1/2', 'z+1/2,-x,-y', '-z,x+1/2,-y', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z,-x', '-y,z+1/2,-x', '-y,-z,x+1/2', '-x,-y,-z', 'x+1/2,y+1/2,-z', '-x,y+1/2,z+1/2', 'x+1/2,-y,z+1/2', '-z,-x,-y', 'z+1/2,x+1/2,-y', '-z,x+1/2,y+1/2', 'z+1/2,-x,y+1/2', '-y,-z,-x', '-y,z+1/2,x+1/2', 'y+1/2,-z,x+1/2', 'y+1/2,z+1/2,-x'], 'universal_h_m': 'Im-3(a-1/4,b-1/4,c-1/4)'}, {'hall': '-F 4a 2 3 (x-1/4,y-1/4,z-1/4)', 'hermann_mauguin': 'Fm-3c', 'hermann_mauguin_u': 'Fm-3c', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y,-z', 'y,x,-z', '-x,y,-z', '-y,-x,-z', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x,-y', 'x,z,-y', '-z,x,-y', '-x,-z,-y', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y,-x', '-y,-z,x', 'z,-y,x', '-z,y,x', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z+1/2,-x+1/2,-y+1/2', 'x+1/2,-z+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x+1/2,z+1/2,-y+1/2', '-z+1/2,x+1/2,y+1/2', '-x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x+1/2', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2'], 'number': 226, 'point_group': 'm-3m', 'schoenflies': 'Oh^6', 'short_h_m': 'Fm-3c', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', 'x,-y+1/2,-z+1/2', 'y+1/2,x,-z+1/2', '-x,y+1/2,-z+1/2', '-y+1/2,-x,-z+1/2', 'z,x,y', '-x,z,y', '-z,-x,y', 'x,-z,y', 'z,-x+1/2,-y+1/2', 'x+1/2,z,-y+1/2', '-z,x+1/2,-y+1/2', '-x+1/2,-z,-y+1/2', 'y,z,x', 'y,-z,-x', 'z,y,-x', '-y,z,-x', '-z,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x+1/2', '-z,y+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y+1/2,-x+1/2,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y+1/2,x+1/2,-z+1/2', '-x+1/2,y,z', '-y,-x+1/2,z', 'x+1/2,-y,z', 'y,x+1/2,z', '-z+1/2,-x+1/2,-y+1/2', 'x+1/2,-z+1/2,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x+1/2,z+1/2,-y+1/2', '-z+1/2,x,y', '-x,-z+1/2,y', 'z+1/2,-x,y', 'x,z+1/2,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y,x', 'y,z,-x+1/2', '-z+1/2,y,-x', 'z+1/2,-y,-x', 'x,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y+1/2,z+1/2', 'y,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z', '-x,y,-z', '-y+1/2,-x+1/2,-z', 'z,x+1/2,y+1/2', '-x,z+1/2,y+1/2', '-z,-x+1/2,y+1/2', 'x,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y', '-z,x,-y', '-x+1/2,-z+1/2,-y', 'y,z+1/2,x+1/2', 'y,-z+1/2,-x+1/2', 'z,y+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-z,-y,-x', '-y+1/2,-z,x+1/2', 'z,-y,x', '-z,y,x', '-x+1/2,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y,-z', '-y+1/2,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y,x,z+1/2', '-z+1/2,-x,-y', 'x+1/2,-z,-y', 'z+1/2,x,-y', '-x+1/2,z,-y', '-z+1/2,x+1/2,y+1/2', '-x,-z,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x,z,y+1/2', '-y+1/2,-z,-x', '-y+1/2,z,x', '-z+1/2,-y,x', 'y+1/2,-z,x', 'z+1/2,y+1/2,x+1/2', 'y,z+1/2,-x', '-z+1/2,y+1/2,-x+1/2', 'z+1/2,-y+1/2,-x+1/2', 'x+1/2,y,z+1/2', '-y+1/2,x,z+1/2', '-x+1/2,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y+1/2,-z', 'y,x,-z', '-x+1/2,y+1/2,-z', '-y,-x,-z', 'z+1/2,x,y+1/2', '-x+1/2,z,y+1/2', '-z+1/2,-x,y+1/2', 'x+1/2,-z,y+1/2', 'z+1/2,-x+1/2,-y', 'x,z,-y', '-z+1/2,x+1/2,-y', '-x,-z,-y', 'y+1/2,z,x+1/2', 'y+1/2,-z,-x+1/2', 'z+1/2,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x', '-y,-z+1/2,x+1/2', 'z+1/2,-y+1/2,x', '-z+1/2,y+1/2,x', '-x,-y+1/2,-z', 'y,-x+1/2,-z', 'x,y+1/2,-z', '-y,x+1/2,-z', '-x,y,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x,-y,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z,-x+1/2,-y', 'x,-z+1/2,-y', 'z,x+1/2,-y', '-x,z+1/2,-y', '-z,x,y+1/2', '-x+1/2,-z+1/2,y+1/2', 'z,-x,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y,-z+1/2,-x', '-y,z+1/2,x', '-z,-y+1/2,x', 'y,-z+1/2,x', 'z,y,x+1/2', 'y+1/2,z,-x', '-z,y,-x+1/2', 'z,-y,-x+1/2', 'x+1/2,y+1/2,z', '-y+1/2,x+1/2,z', '-x+1/2,-y+1/2,z', 'y+1/2,-x+1/2,z', 'x+1/2,-y,-z+1/2', 'y,x+1/2,-z+1/2', '-x+1/2,y,-z+1/2', '-y,-x+1/2,-z+1/2', 'z+1/2,x+1/2,y', '-x+1/2,z+1/2,y', '-z+1/2,-x+1/2,y', 'x+1/2,-z+1/2,y', 'z+1/2,-x,-y+1/2', 'x,z+1/2,-y+1/2', '-z+1/2,x,-y+1/2', '-x,-z+1/2,-y+1/2', 'y+1/2,z+1/2,x', 'y+1/2,-z+1/2,-x', 'z+1/2,y+1/2,-x', '-y+1/2,z+1/2,-x', '-z+1/2,-y,-x+1/2', '-y,-z,x', 'z+1/2,-y,x+1/2', '-z+1/2,y,x+1/2', '-x,-y,-z+1/2', 'y,-x,-z+1/2', 'x,y,-z+1/2', '-y,x,-z+1/2', '-x,y+1/2,z', '-y+1/2,-x,z', 'x,-y+1/2,z', 'y+1/2,x,z', '-z,-x,-y+1/2', 'x,-z,-y+1/2', 'z,x,-y+1/2', '-x,z,-y+1/2', '-z,x+1/2,y', '-x+1/2,-z,y', 'z,-x+1/2,y', 'x+1/2,z,y', '-y,-z,-x+1/2', '-y,z,x+1/2', '-z,-y,x+1/2', 'y,-z,x+1/2', 'z,y+1/2,x', 'y+1/2,z+1/2,-x+1/2', '-z,y+1/2,-x', 'z,-y+1/2,-x'], 'universal_h_m': 'Fm-3c(a+1/4,b+1/4,c+1/4)'}, {'hall': '-I 4 2 3 (x+1/4,y+1/4,z+1/4)', 'hermann_mauguin': 'Im-3m', 'hermann_mauguin_u': 'Im-3m', 'ncsym': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x+1/2,-y+1/2', 'x,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x', '-z+1/2,y,x', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z,-x,-y', 'x+1/2,-z,-y', 'z+1/2,x+1/2,-y', '-x,z+1/2,-y', '-z,x+1/2,y+1/2', '-x,-z,y+1/2', 'z+1/2,-x,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y,-z,-x', '-y,z+1/2,x+1/2', '-z,-y,x+1/2', 'y+1/2,-z,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x', '-z,y+1/2,-x', 'z+1/2,-y,-x'], 'number': 229, 'point_group': 'm-3m', 'schoenflies': 'Oh^9', 'short_h_m': 'Im-3m', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x+1/2,-y+1/2', 'x,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x', '-z+1/2,y,x', '-x+1/2,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x,-z+1/2', '-x+1/2,y,z', '-y+1/2,-x+1/2,z', 'x,-y+1/2,z', 'y,x,z', '-z+1/2,-x+1/2,-y+1/2', 'x,-z+1/2,-y+1/2', 'z,x,-y+1/2', '-x+1/2,z,-y+1/2', '-z+1/2,x,y', '-x+1/2,-z+1/2,y', 'z,-x+1/2,y', 'x,z,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z,x', '-z+1/2,-y+1/2,x', 'y,-z+1/2,x', 'z,y,x', 'y,z,-x+1/2', '-z+1/2,y,-x+1/2', 'z,-y+1/2,-x+1/2', 'x+1/2,y+1/2,z+1/2', '-y,x+1/2,z+1/2', '-x,-y,z+1/2', 'y+1/2,-x,z+1/2', 'x+1/2,-y,-z', 'y+1/2,x+1/2,-z', '-x,y+1/2,-z', '-y,-x,-z', 'z+1/2,x+1/2,y+1/2', '-x,z+1/2,y+1/2', '-z,-x,y+1/2', 'x+1/2,-z,y+1/2', 'z+1/2,-x,-y', 'x+1/2,z+1/2,-y', '-z,x+1/2,-y', '-x,-z,-y', 'y+1/2,z+1/2,x+1/2', 'y+1/2,-z,-x', 'z+1/2,y+1/2,-x', '-y,z+1/2,-x', '-z,-y,-x', '-y,-z,x+1/2', 'z+1/2,-y,x+1/2', '-z,y+1/2,x+1/2', '-x,-y,-z', 'y+1/2,-x,-z', 'x+1/2,y+1/2,-z', '-y,x+1/2,-z', '-x,y+1/2,z+1/2', '-y,-x,z+1/2', 'x+1/2,-y,z+1/2', 'y+1/2,x+1/2,z+1/2', '-z,-x,-y', 'x+1/2,-z,-y', 'z+1/2,x+1/2,-y', '-x,z+1/2,-y', '-z,x+1/2,y+1/2', '-x,-z,y+1/2', 'z+1/2,-x,y+1/2', 'x+1/2,z+1/2,y+1/2', '-y,-z,-x', '-y,z+1/2,x+1/2', '-z,-y,x+1/2', 'y+1/2,-z,x+1/2', 'z+1/2,y+1/2,x+1/2', 'y+1/2,z+1/2,-x', '-z,y+1/2,-x', 'z+1/2,-y,-x'], 'universal_h_m': 'Im-3m(a-1/4,b-1/4,c-1/4)'}, {'hall': '-F 4 2 3 (x+1/4,y+1/4,z+1/4)', 'hermann_mauguin': 'Fm-3m', 'hermann_mauguin_u': 'Fm-3m', 'ncsym': ['x,y,z', '-y+1/2,x+1/2,z+1/2', '-x,-y,z', 'y+1/2,-x+1/2,z+1/2', 'x,-y,-z', 'y+1/2,x+1/2,-z+1/2', '-x,y,-z', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z+1/2,y+1/2', '-z,-x,y', 'x+1/2,-z+1/2,y+1/2', 'z,-x,-y', 'x+1/2,z+1/2,-y+1/2', '-z,x,-y', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z,-x', 'z+1/2,y+1/2,-x+1/2', '-y,z,-x', '-z+1/2,-y+1/2,-x+1/2', '-y,-z,x', 'z+1/2,-y+1/2,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x+1/2,-y+1/2,-z+1/2', 'y,-x,-z', 'x+1/2,y+1/2,-z+1/2', '-y,x,-z', '-x+1/2,y+1/2,z+1/2', '-y,-x,z', 'x+1/2,-y+1/2,z+1/2', 'y,x,z', '-z+1/2,-x+1/2,-y+1/2', 'x,-z,-y', 'z+1/2,x+1/2,-y+1/2', '-x,z,-y', '-z+1/2,x+1/2,y+1/2', '-x,-z,y', 'z+1/2,-x+1/2,y+1/2', 'x,z,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z+1/2,x+1/2', '-z,-y,x', 'y+1/2,-z+1/2,x+1/2', 'z,y,x', 'y+1/2,z+1/2,-x+1/2', '-z,y,-x', 'z,-y,-x'], 'number': 225, 'point_group': 'm-3m', 'schoenflies': 'Oh^5', 'short_h_m': 'Fm-3m', 'symops': ['x,y,z', '-y+1/2,x,z', '-x+1/2,-y+1/2,z', 'y,-x+1/2,z', 'x,-y+1/2,-z+1/2', 'y,x,-z+1/2', '-x+1/2,y,-z+1/2', '-y+1/2,-x+1/2,-z+1/2', 'z,x,y', '-x+1/2,z,y', '-z+1/2,-x+1/2,y', 'x,-z+1/2,y', 'z,-x+1/2,-y+1/2', 'x,z,-y+1/2', '-z+1/2,x,-y+1/2', '-x+1/2,-z+1/2,-y+1/2', 'y,z,x', 'y,-z+1/2,-x+1/2', 'z,y,-x+1/2', '-y+1/2,z,-x+1/2', '-z+1/2,-y+1/2,-x+1/2', '-y+1/2,-z+1/2,x', 'z,-y+1/2,x', '-z+1/2,y,x', '-x+1/2,-y+1/2,-z+1/2', 'y,-x+1/2,-z+1/2', 'x,y,-z+1/2', '-y+1/2,x,-z+1/2', '-x+1/2,y,z', '-y+1/2,-x+1/2,z', 'x,-y+1/2,z', 'y,x,z', '-z+1/2,-x+1/2,-y+1/2', 'x,-z+1/2,-y+1/2', 'z,x,-y+1/2', '-x+1/2,z,-y+1/2', '-z+1/2,x,y', '-x+1/2,-z+1/2,y', 'z,-x+1/2,y', 'x,z,y', '-y+1/2,-z+1/2,-x+1/2', '-y+1/2,z,x', '-z+1/2,-y+1/2,x', 'y,-z+1/2,x', 'z,y,x', 'y,z,-x+1/2', '-z+1/2,y,-x+1/2', 'z,-y+1/2,-x+1/2', 'x,y+1/2,z+1/2', '-y+1/2,x+1/2,z+1/2', '-x+1/2,-y,z+1/2', 'y,-x,z+1/2', 'x,-y,-z', 'y,x+1/2,-z', '-x+1/2,y+1/2,-z', '-y+1/2,-x,-z', 'z,x+1/2,y+1/2', '-x+1/2,z+1/2,y+1/2', '-z+1/2,-x,y+1/2', 'x,-z,y+1/2', 'z,-x,-y', 'x,z+1/2,-y', '-z+1/2,x+1/2,-y', '-x+1/2,-z,-y', 'y,z+1/2,x+1/2', 'y,-z,-x', 'z,y+1/2,-x', '-y+1/2,z+1/2,-x', '-z+1/2,-y,-x', '-y+1/2,-z,x+1/2', 'z,-y,x+1/2', '-z+1/2,y+1/2,x+1/2', '-x+1/2,-y,-z', 'y,-x,-z', 'x,y+1/2,-z', '-y+1/2,x+1/2,-z', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x,z+1/2', 'x,-y,z+1/2', 'y,x+1/2,z+1/2', '-z+1/2,-x,-y', 'x,-z,-y', 'z,x+1/2,-y', '-x+1/2,z+1/2,-y', '-z+1/2,x+1/2,y+1/2', '-x+1/2,-z,y+1/2', 'z,-x,y+1/2', 'x,z+1/2,y+1/2', '-y+1/2,-z,-x', '-y+1/2,z+1/2,x+1/2', '-z+1/2,-y,x+1/2', 'y,-z,x+1/2', 'z,y+1/2,x+1/2', 'y,z+1/2,-x', '-z+1/2,y+1/2,-x', 'z,-y,-x', 'x+1/2,y,z+1/2', '-y,x,z+1/2', '-x,-y+1/2,z+1/2', 'y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,-z', 'y+1/2,x,-z', '-x,y,-z', '-y,-x+1/2,-z', 'z+1/2,x,y+1/2', '-x,z,y+1/2', '-z,-x+1/2,y+1/2', 'x+1/2,-z+1/2,y+1/2', 'z+1/2,-x+1/2,-y', 'x+1/2,z,-y', '-z,x,-y', '-x,-z+1/2,-y', 'y+1/2,z,x+1/2', 'y+1/2,-z+1/2,-x', 'z+1/2,y,-x', '-y,z,-x', '-z,-y+1/2,-x', '-y,-z+1/2,x+1/2', 'z+1/2,-y+1/2,x+1/2', '-z,y,x+1/2', '-x,-y+1/2,-z', 'y+1/2,-x+1/2,-z', 'x+1/2,y,-z', '-y,x,-z', '-x,y,z+1/2', '-y,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x,z+1/2', '-z,-x+1/2,-y', 'x+1/2,-z+1/2,-y', 'z+1/2,x,-y', '-x,z,-y', '-z,x,y+1/2', '-x,-z+1/2,y+1/2', 'z+1/2,-x+1/2,y+1/2', 'x+1/2,z,y+1/2', '-y,-z+1/2,-x', '-y,z,x+1/2', '-z,-y+1/2,x+1/2', 'y+1/2,-z+1/2,x+1/2', 'z+1/2,y,x+1/2', 'y+1/2,z,-x', '-z,y,-x', 'z+1/2,-y+1/2,-x', 'x+1/2,y+1/2,z', '-y,x+1/2,z', '-x,-y,z', 'y+1/2,-x,z', 'x+1/2,-y,-z+1/2', 'y+1/2,x+1/2,-z+1/2', '-x,y+1/2,-z+1/2', '-y,-x,-z+1/2', 'z+1/2,x+1/2,y', '-x,z+1/2,y', '-z,-x,y', 'x+1/2,-z,y', 'z+1/2,-x,-y+1/2', 'x+1/2,z+1/2,-y+1/2', '-z,x+1/2,-y+1/2', '-x,-z,-y+1/2', 'y+1/2,z+1/2,x', 'y+1/2,-z,-x+1/2', 'z+1/2,y+1/2,-x+1/2', '-y,z+1/2,-x+1/2', '-z,-y,-x+1/2', '-y,-z,x', 'z+1/2,-y,x', '-z,y+1/2,x', '-x,-y,-z+1/2', 'y+1/2,-x,-z+1/2', 'x+1/2,y+1/2,-z+1/2', '-y,x+1/2,-z+1/2', '-x,y+1/2,z', '-y,-x,z', 'x+1/2,-y,z', 'y+1/2,x+1/2,z', '-z,-x,-y+1/2', 'x+1/2,-z,-y+1/2', 'z+1/2,x+1/2,-y+1/2', '-x,z+1/2,-y+1/2', '-z,x+1/2,y', '-x,-z,y', 'z+1/2,-x,y', 'x+1/2,z+1/2,y', '-y,-z,-x+1/2', '-y,z+1/2,x', '-z,-y,x', 'y+1/2,-z,x', 'z+1/2,y+1/2,x', 'y+1/2,z+1/2,-x+1/2', '-z,y+1/2,-x+1/2', 'z+1/2,-y,-x+1/2'], 'universal_h_m': 'Fm-3m(a-1/4,b-1/4,c-1/4)'}, {'hall': ' P 4 -2ab (x,y,1/2*z)', 'hermann_mauguin': 'P4bm', 'hermann_mauguin_u': 'P4bm', 'ncsym': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z', 'x,y,z+1/2', '-y,x,z+1/2', '-x,-y,z+1/2', 'y,-x,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'number': 100, 'point_group': '4mm', 'schoenflies': 'C4v^2', 'short_h_m': 'P4bm', 'symops': ['x,y,z', '-y,x,z', '-x,-y,z', 'y,-x,z', '-x+1/2,y+1/2,z', '-y+1/2,-x+1/2,z', 'x+1/2,-y+1/2,z', 'y+1/2,x+1/2,z', 'x,y,z+1/2', '-y,x,z+1/2', '-x,-y,z+1/2', 'y,-x,z+1/2', '-x+1/2,y+1/2,z+1/2', '-y+1/2,-x+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'y+1/2,x+1/2,z+1/2'], 'universal_h_m': 'P4bm(a,b,2*c)'}, {'hall': ' C -2yc (1/2*x,y,-1/2*x+z)', 'hermann_mauguin': 'C1c1', 'hermann_mauguin_u': 'C1c1', 'ncsym': ['x,y,z', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,-y,z'], 'number': 9, 'point_group': 'm', 'schoenflies': 'Cs^4', 'short_h_m': 'Cc', 'symops': ['x,y,z', 'x,-y,z+1/2', 'x+1/2,y,z+1/2', 'x+1/2,-y,z', 'x+1/4,y+1/2,z+3/4', 'x+1/4,-y+1/2,z+1/4', 'x+3/4,y+1/2,z+1/4', 'x+3/4,-y+1/2,z+3/4'], 'universal_h_m': 'C1c1(2*a+c,b,c)'}, {'hall': ' P 2c -2 (1/2*x,y,z)', 'hermann_mauguin': 'Pmc21', 'hermann_mauguin_u': 'Pmc2_1', 'ncsym': ['x,y,z', '-x,y,z', 'x,-y,z+1/2', '-x,-y,z+1/2'], 'number': 26, 'point_group': 'mm2', 'schoenflies': 'C2v^2', 'short_h_m': 'Pmc2_1', 'symops': ['x,y,z', '-x,y,z', 'x,-y,z+1/2', '-x,-y,z+1/2', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,-y,z+1/2', '-x+1/2,-y,z+1/2'], 'universal_h_m': 'Pmc21(2*a,b,c)'}, {'hall': ' C 2 -2 (1/2*z,x,y)', 'hermann_mauguin': 'Cmm2', 'hermann_mauguin_u': 'Cmm2', 'ncsym': ['x,y,z', 'x,-y,z', 'x,y,-z', 'x,-y,-z'], 'number': 35, 'point_group': 'mm2', 'schoenflies': 'C2v^11', 'short_h_m': 'Cmm2', 'symops': ['x,y,z', 'x,-y,z', 'x,y,-z', 'x,-y,-z', 'x,y+1/2,z+1/2', 'x,-y+1/2,z+1/2', 'x,y+1/2,-z+1/2', 'x,-y+1/2,-z+1/2', 'x+1/2,y,z', 'x+1/2,-y,z', 'x+1/2,y,-z', 'x+1/2,-y,-z', 'x+1/2,y+1/2,z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x+1/2,y+1/2,-z+1/2', 'x+1/2,-y+1/2,-z+1/2'], 'universal_h_m': 'Cmm2(2*c,a,b)'}, {'hall': '-P 2ybc (-1/4*x+1/2*z,1/2*x,y)', 'hermann_mauguin': 'P121/c1', 'hermann_mauguin_u': 'P12_1/c1', 'ncsym': ['x,y,z', '-x+1/4,-y,z+1/2', '-x,-y,-z', 'x-1/4,y,-z-1/2'], 'number': 14, 'point_group': '2/m', 'schoenflies': 'C2h^5', 'short_h_m': 'P2_1/c', 'symops': ['x,y,z', '-x+1/4,-y,z+1/2', '-x,-y,-z', 'x-1/4,y,-z-1/2', 'x+3/4,y+1/2,z', '-x+1,-y+1/2,z+1/2', '-x+3/4,-y+1/2,-z', 'x+1/2,y+1/2,-z-1/2', 'x+1/4,y+1/2,z', '-x+1/2,-y+1/2,z+1/2', '-x+1/4,-y+1/2,-z', 'x,y+1/2,-z-1/2', 'x+1/2,y,z', '-x+3/4,-y,z+1/2', '-x+1/2,-y,-z', 'x+1/4,y,-z-1/2'], 'universal_h_m': 'P121/c1(2*c,2*a+c,b)'}, {'hall': '-P 2a 2a (1/2*y,z,x)', 'hermann_mauguin': 'Pmma', 'hermann_mauguin_u': 'Pmma', 'ncsym': ['x,y,z', '-x,y,z', 'x,y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,-z', '-x,-y,z-1/2', 'x,-y,z-1/2'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmma', 'symops': ['x,y,z', '-x,y,z', 'x,y,-z+1/2', '-x,y,-z+1/2', '-x,-y,-z', 'x,-y,-z', '-x,-y,z-1/2', 'x,-y,z-1/2', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,y,-z+1/2', '-x+1/2,y,-z+1/2', '-x+1/2,-y,-z', 'x+1/2,-y,-z', '-x+1/2,-y,z-1/2', 'x+1/2,-y,z-1/2'], 'universal_h_m': 'Pmma(2*b,c,a)'}, {'hall': '-P 2a 2a (1/2*y,z+1/3,x-1/4)', 'hermann_mauguin': 'Pmma', 'hermann_mauguin_u': 'Pmma', 'ncsym': ['x,y,z', '-x,y,z', 'x,y,-z', '-x,y,-z', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,y,-z', '-x+1/2,y,-z'], 'number': 51, 'point_group': 'mmm', 'schoenflies': 'D2h^5', 'short_h_m': 'Pmma', 'symops': ['x,y,z', '-x,y,z', 'x,y,-z', '-x,y,-z', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,y,-z', '-x+1/2,y,-z', '-x,-y+2/3,-z+1/2', 'x,-y+2/3,-z+1/2', '-x,-y+2/3,z+1/2', 'x,-y+2/3,z+1/2', '-x+1/2,-y+2/3,-z+1/2', 'x+1/2,-y+2/3,-z+1/2', '-x+1/2,-y+2/3,z+1/2', 'x+1/2,-y+2/3,z+1/2'], 'universal_h_m': 'Pmma(2*b+1/4,c,a-1/3)'}, {'hall': '-P 2yc (x,1/2*y,z)', 'hermann_mauguin': 'P12/c1', 'hermann_mauguin_u': 'P12/c1', 'ncsym': ['x,y,z', '-x,y,-z+1/2', 'x,y+1/2,z', '-x,y+1/2,-z+1/2'], 'number': 13, 'point_group': '2/m', 'schoenflies': 'C2h^4', 'short_h_m': 'P2/c', 'symops': ['x,y,z', '-x,y,-z+1/2', 'x,y+1/2,z', '-x,y+1/2,-z+1/2', '-x,-y,-z', 'x,-y,z+1/2', '-x,-y+1/2,-z', 'x,-y+1/2,z+1/2'], 'universal_h_m': 'P12/c1(a,2*b,c)'}, {'hall': '-P 2 2 (1/2*x,1/2*y,z)', 'hermann_mauguin': 'Pmmm', 'hermann_mauguin_u': 'Pmmm', 'ncsym': ['x,y,z', '-x,y,z', 'x,-y,z', '-x,-y,z', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,-y,z', '-x+1/2,-y,z'], 'number': 47, 'point_group': 'mmm', 'schoenflies': 'D2h^1', 'short_h_m': 'Pmmm', 'symops': ['x,y,z', '-x,y,z', 'x,-y,z', '-x,-y,z', 'x+1/2,y,z', '-x+1/2,y,z', 'x+1/2,-y,z', '-x+1/2,-y,z', 'x,y+1/2,z', '-x,y+1/2,z', 'x,-y+1/2,z', '-x,-y+1/2,z', 'x+1/2,y+1/2,z', '-x+1/2,y+1/2,z', 'x+1/2,-y+1/2,z', '-x+1/2,-y+1/2,z', '-x,-y,-z', 'x,-y,-z', '-x,y,-z', 'x,y,-z', '-x+1/2,-y,-z', 'x+1/2,-y,-z', '-x+1/2,y,-z', 'x+1/2,y,-z', '-x,-y+1/2,-z', 'x,-y+1/2,-z', '-x,y+1/2,-z', 'x,y+1/2,-z', '-x+1/2,-y+1/2,-z', 'x+1/2,-y+1/2,-z', '-x+1/2,y+1/2,-z', 'x+1/2,y+1/2,-z'], 'universal_h_m': 'Pmmm(2*a,2*b,c)'}, {'hall': ' P 2yb (x+1/4,y,z)', 'hermann_mauguin': 'P1211', 'hermann_mauguin_u': 'P12_11', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z'], 'number': 4, 'point_group': '2', 'schoenflies': 'C2^2', 'short_h_m': 'P2_1', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z'], 'universal_h_m': 'P1211(a-1/4,b,c)'}, {'hall': '-P 2ac 2n (z,x,y+1/4)', 'hermann_mauguin': 'Pnma', 'hermann_mauguin_u': 'Pnma', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y,-z', '-x+1/2,y+1/2,z'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pnma', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y,-z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'Pnma(c,a-1/4,b)'}][source]

abbrev_sg_mapping = {'C2': 'C121', 'C2/c': 'C12/c1', 'C2/m': 'C12/m1', 'Cc': 'C1c1', 'Cm': 'C1m1', 'P2': 'P121', 'P2/c': 'P12/c1', 'P2/m': 'P12/m1', 'P2_1': 'P12_11', 'P2_1/c': 'P12_1/c1', 'P2_1/m': 'P12_1/m1', 'Pc': 'P1c1', 'Pm': 'P1m1'}[source]

property crystal_system: CrystalSystem[source]

Returns: str: Crystal system of the space group, e.g. cubic, hexagonal, etc.

classmethod from_int_number(int_number: int, hexagonal: bool = True) → Self[source]

Obtains a SpaceGroup from its international number.

Parameters:

• int_number (int) – International number.

• hexagonal (bool) – For rhombohedral groups, whether to return the hexagonal setting (default) or rhombohedral setting.

Raises:

ValueError – If the international number is not valid, i.e. not between 1 and 230 inclusive.

Returns:

object with the given international number.

Return type:

SpaceGroup

full_sg_mapping: ClassVar[dict[str, str]] = {'Aea2': 'Aea2', 'Aem2': 'Aem2', 'Ama2': 'Ama2', 'Amm2': 'Amm2', 'C12/c1': 'C12/c1', 'C12/m1': 'C12/m1', 'C121': 'C121', 'C1c1': 'C1c1', 'C1m1': 'C1m1', 'C2/c2/c2/e': 'Ccce', 'C2/c2/c2/m': 'Cccm', 'C2/m2/c2_1/e': 'Cmce', 'C2/m2/c2_1/m': 'Cmcm', 'C2/m2/m2/e': 'Cmme', 'C2/m2/m2/m': 'Cmmm', 'C222': 'C222', 'C222_1': 'C222_1', 'Ccc2': 'Ccc2', 'Cmc2_1': 'Cmc2_1', 'Cmm2': 'Cmm2', 'F-43c': 'F-43c', 'F-43m': 'F-43m', 'F2/d-3': 'Fd-3', 'F2/d2/d2/d': 'Fddd', 'F2/m-3': 'Fm-3', 'F2/m2/m2/m': 'Fmmm', 'F222': 'F222', 'F23': 'F23', 'F4/m-32/c': 'Fm-3c', 'F4/m-32/m': 'Fm-3m', 'F432': 'F432', 'F4_1/d-32/c': 'Fd-3c', 'F4_1/d-32/m': 'Fd-3m', 'F4_132': 'F4_132', 'Fdd2': 'Fdd2', 'Fmm2': 'Fmm2', 'I-4': 'I-4', 'I-42d': 'I-42d', 'I-42m': 'I-42m', 'I-43d': 'I-43d', 'I-43m': 'I-43m', 'I-4c2': 'I-4c2', 'I-4m2': 'I-4m2', 'I2/b2/a2/m': 'Ibam', 'I2/m-3': 'Im-3', 'I2/m2/m2/m': 'Immm', 'I222': 'I222', 'I23': 'I23', 'I2_1/a-3': 'Ia-3', 'I2_1/b2_1/c2_1/a': 'Ibca', 'I2_1/m2_1/m2_1/a': 'Imma', 'I2_12_12_1': 'I2_12_12_1', 'I2_13': 'I2_13', 'I4': 'I4', 'I4/m': 'I4/m', 'I4/m-32/m': 'Im-3m', 'I4/m2/c2/m': 'I4/mcm', 'I4/m2/m2/m': 'I4/mmm', 'I422': 'I422', 'I432': 'I432', 'I4_1': 'I4_1', 'I4_1/a': 'I4_1/a', 'I4_1/a-32/d': 'Ia-3d', 'I4_1/a2/c2/d': 'I4_1/acd', 'I4_1/a2/m2/d': 'I4_1/amd', 'I4_122': 'I4_122', 'I4_132': 'I4_132', 'I4_1cd': 'I4_1cd', 'I4_1md': 'I4_1md', 'I4cm': 'I4cm', 'I4mm': 'I4mm', 'Iba2': 'Iba2', 'Ima2': 'Ima2', 'Imm2': 'Imm2', 'P-1': 'P-1', 'P-3': 'P-3', 'P-312/c': 'P-31c', 'P-312/m': 'P-31m', 'P-32/c1': 'P-3c1', 'P-32/m1': 'P-3m1', 'P-4': 'P-4', 'P-42_1c': 'P-42_1c', 'P-42_1m': 'P-42_1m', 'P-42c': 'P-42c', 'P-42m': 'P-42m', 'P-43m': 'P-43m', 'P-43n': 'P-43n', 'P-4b2': 'P-4b2', 'P-4c2': 'P-4c2', 'P-4m2': 'P-4m2', 'P-4n2': 'P-4n2', 'P-6': 'P-6', 'P-62c': 'P-62c', 'P-62m': 'P-62m', 'P-6c2': 'P-6c2', 'P-6m2': 'P-6m2', 'P1': 'P1', 'P12/c1': 'P12/c1', 'P12/m1': 'P12/m1', 'P121': 'P121', 'P12_1/c1': 'P12_1/c1', 'P12_1/m1': 'P12_1/m1', 'P12_11': 'P12_11', 'P1c1': 'P1c1', 'P1m1': 'P1m1', 'P2/b2/a2/n': 'Pban', 'P2/b2_1/c2_1/m': 'Pbcm', 'P2/c2/c2/m': 'Pccm', 'P2/m-3': 'Pm-3', 'P2/m2/m2/m': 'Pmmm', 'P2/m2/n2_1/a': 'Pmna', 'P2/n-3': 'Pn-3', 'P2/n2/n2/n': 'Pnnn', 'P2/n2_1/n2/a': 'Pnna', 'P222': 'P222', 'P222_1': 'P222_1', 'P23': 'P23', 'P2_1/a-3': 'Pa-3', 'P2_1/b2/c2_1/n': 'Pbcn', 'P2_1/b2_1/a2/m': 'Pbam', 'P2_1/b2_1/c2_1/a': 'Pbca', 'P2_1/c2/c2/a': 'Pcca', 'P2_1/c2_1/c2/n': 'Pccn', 'P2_1/m2/m2/a': 'Pmma', 'P2_1/m2_1/m2/n': 'Pmmn', 'P2_1/n2_1/m2_1/a': 'Pnma', 'P2_1/n2_1/n2/m': 'Pnnm', 'P2_12_12': 'P2_12_12', 'P2_12_12_1': 'P2_12_12_1', 'P2_13': 'P2_13', 'P3': 'P3', 'P312': 'P312', 'P31c': 'P31c', 'P31m': 'P31m', 'P321': 'P321', 'P3_1': 'P3_1', 'P3_112': 'P3_112', 'P3_121': 'P3_121', 'P3_2': 'P3_2', 'P3_212': 'P3_212', 'P3_221': 'P3_221', 'P3c1': 'P3c1', 'P3m1': 'P3m1', 'P4': 'P4', 'P4/m': 'P4/m', 'P4/m-32/m': 'Pm-3m', 'P4/m2/c2/c': 'P4/mcc', 'P4/m2/m2/m': 'P4/mmm', 'P4/m2_1/b2/m': 'P4/mbm', 'P4/m2_1/n2/c': 'P4/mnc', 'P4/n': 'P4/n', 'P4/n-32/n': 'Pn-3n', 'P4/n2/b2/m': 'P4/nbm', 'P4/n2/n2/c': 'P4/nnc', 'P4/n2_1/c2/c': 'P4/ncc', 'P4/n2_1/m2/m': 'P4/nmm', 'P422': 'P422', 'P42_12': 'P42_12', 'P432': 'P432', 'P4_1': 'P4_1', 'P4_122': 'P4_122', 'P4_12_12': 'P4_12_12', 'P4_132': 'P4_132', 'P4_2': 'P4_2', 'P4_2/m': 'P4_2/m', 'P4_2/m-32/n': 'Pm-3n', 'P4_2/m2/c2/m': 'P4_2/mcm', 'P4_2/m2/m2/c': 'P4_2/mmc', 'P4_2/m2_1/b2/c': 'P4_2/mbc', 'P4_2/m2_1/n2/m': 'P4_2/mnm', 'P4_2/n': 'P4_2/n', 'P4_2/n-32/m': 'Pn-3m', 'P4_2/n2/b2/c': 'P4_2/nbc', 'P4_2/n2/n2/m': 'P4_2/nnm', 'P4_2/n2_1/c2/m': 'P4_2/ncm', 'P4_2/n2_1/m2/c': 'P4_2/nmc', 'P4_222': 'P4_222', 'P4_22_12': 'P4_22_12', 'P4_232': 'P4_232', 'P4_2bc': 'P4_2bc', 'P4_2cm': 'P4_2cm', 'P4_2mc': 'P4_2mc', 'P4_2nm': 'P4_2nm', 'P4_3': 'P4_3', 'P4_322': 'P4_322', 'P4_32_12': 'P4_32_12', 'P4_332': 'P4_332', 'P4bm': 'P4bm', 'P4cc': 'P4cc', 'P4mm': 'P4mm', 'P4nc': 'P4nc', 'P6': 'P6', 'P6/m': 'P6/m', 'P6/m2/c2/c': 'P6/mcc', 'P6/m2/m2/m': 'P6/mmm', 'P622': 'P622', 'P6_1': 'P6_1', 'P6_122': 'P6_122', 'P6_2': 'P6_2', 'P6_222': 'P6_222', 'P6_3': 'P6_3', 'P6_3/m': 'P6_3/m', 'P6_3/m2/c2/m': 'P6_3/mcm', 'P6_3/m2/m2/c': 'P6_3/mmc', 'P6_322': 'P6_322', 'P6_3cm': 'P6_3cm', 'P6_3mc': 'P6_3mc', 'P6_4': 'P6_4', 'P6_422': 'P6_422', 'P6_5': 'P6_5', 'P6_522': 'P6_522', 'P6cc': 'P6cc', 'P6mm': 'P6mm', 'Pba2': 'Pba2', 'Pca2_1': 'Pca2_1', 'Pcc2': 'Pcc2', 'Pma2': 'Pma2', 'Pmc2_1': 'Pmc2_1', 'Pmm2': 'Pmm2', 'Pmn2_1': 'Pmn2_1', 'Pna2_1': 'Pna2_1', 'Pnc2': 'Pnc2', 'Pnn2': 'Pnn2', 'R-3': 'R-3', 'R-32/c': 'R-3c', 'R-32/m': 'R-3m', 'R3': 'R3', 'R32': 'R32', 'R3c': 'R3c', 'R3m': 'R3m'}[source]

gen_matrices = {'a': [[1, 0, 0], [0, 1, 0], [0, 0, 1]], 'b': [[-1, 0, 0], [0, -1, 0], [0, 0, 1]], 'c': [[-1, 0, 0], [0, 1, 0], [0, 0, -1]], 'd': [[0, 0, 1], [1, 0, 0], [0, 1, 0]], 'e': [[0, 1, 0], [1, 0, 0], [0, 0, -1]], 'f': [[0, -1, 0], [-1, 0, 0], [0, 0, -1]], 'g': [[0, -1, 0], [1, 0, 0], [0, 0, 1]], 'h': [[-1, 0, 0], [0, -1, 0], [0, 0, -1]], 'i': [[1, 0, 0], [0, 1, 0], [0, 0, -1]], 'j': [[1, 0, 0], [0, -1, 0], [0, 0, 1]], 'k': [[0, -1, 0], [-1, 0, 0], [0, 0, 1]], 'l': [[0, 1, 0], [1, 0, 0], [0, 0, 1]], 'm': [[0, 1, 0], [-1, 0, 0], [0, 0, -1]], 'n': [[0, -1, 0], [1, -1, 0], [0, 0, 1]]}[source]

get_orbit(p: ArrayLike, tol: float = 1e-05) → list[np.ndarray][source]

Get the orbit for a point.

Parameters:

• p – Point as a 3x1 array.

• tol – Tolerance for determining if sites are the same. 1e-5 should be sufficient for most purposes. Set to 0 for exact matching (and also needed for symbolic orbits).

Returns:

Orbit for point.

Return type:

list[array]

get_orbit_and_generators(p: ArrayLike, tol: float = 1e-05) → tuple[list[np.ndarray], list[SymmOp]][source]

Get the orbit and its generators for a point.

Parameters:

• p – Point as a 3x1 array.

• tol – Tolerance for determining if sites are the same. 1e-5 should be sufficient for most purposes. Set to 0 for exact matching (and also needed for symbolic orbits).

Returns:

Orbit and generators for point.

Return type:

tuple[list[np.ndarray], list[SymmOp]]

classmethod get_settings(int_symbol: str) → set[str][source]

Get all the settings for a particular international symbol.

Parameters:

int_symbol (str) – Full International (e.g., “P2/m2/m2/m”) or Hermann-Mauguin Symbol (“Pmmm”) or abbreviated symbol. The notation is a LaTeX-like string, with screw axes being represented by an underscore. For example, “P6_3/mmc”.

Returns:

All possible settings for the given international symbol.

Return type:

set[str]

is_compatible(lattice: Lattice, tol: float = 1e-05, angle_tol: float = 5) → bool[source]

Check whether a particular lattice is compatible with the conventional unit cell.

Parameters:

• lattice (Lattice) – A Lattice.

• tol (float) – The tolerance to check for equality of lengths.

• angle_tol (float) – The tolerance to check for equality of angles in degrees.

is_subgroup(supergroup: SymmetryGroup) → bool[source]

Check if space group is a subgroup of the supplied symmetry group.

Parameters:

supergroup (Spacegroup) – Supergroup to test.

Returns:

True if this space group is a subgroup of the supplied group.

Return type:

bool

is_supergroup(subgroup: SymmetryGroup) → bool[source]

True if this space group is a supergroup of the supplied group.

Parameters:

subgroup (Spacegroup) – Subgroup to test.

Returns:

True if this space group is a supergroup of the supplied group.

Return type:

bool

op = {'hall': '-P 2ac 2n (z,x,y+1/4)', 'hermann_mauguin': 'Pnma', 'hermann_mauguin_u': 'Pnma', 'ncsym': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y,-z', '-x+1/2,y+1/2,z'], 'number': 62, 'point_group': 'mmm', 'schoenflies': 'D2h^16', 'short_h_m': 'Pnma', 'symops': ['x,y,z', '-x+1/2,y+1/2,-z', '-x,-y,z+1/2', 'x+1/2,-y+1/2,-z+1/2', '-x,-y,-z+1/2', 'x+1/2,-y+1/2,z+1/2', 'x,y,-z', '-x+1/2,y+1/2,z'], 'universal_h_m': 'Pnma(c,a-1/4,b)'}[source]

sg_encoding = {'Aba2': {'enc': '03aODDbOOOjDDO0', 'full_symbol': 'Aea2', 'int_number': 41, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'Abm2': {'enc': '03aODDbOOOjODO0', 'full_symbol': 'Aem2', 'int_number': 39, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'Aea2': {'enc': '03aODDbOOOjDDO0', 'full_symbol': 'Aea2', 'int_number': 41, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'Aem2': {'enc': '03aODDbOOOjODO0', 'full_symbol': 'Aem2', 'int_number': 39, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'Ama2': {'enc': '03aODDbOOOjDOO0', 'full_symbol': 'Ama2', 'int_number': 40, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'Amm2': {'enc': '03aODDbOOOjOOO0', 'full_symbol': 'Amm2', 'int_number': 38, 'order': 8, 'patterson_symmetry': 'Ammm (Cmmm)', 'point_group': 'mm2'}, 'C12/c1': {'enc': '12aDDOcOOD0', 'full_symbol': 'C12/c1', 'int_number': 15, 'order': 8, 'patterson_symmetry': 'C12/m1', 'point_group': '2/m'}, 'C12/m1': {'enc': '12aDDOcOOO0', 'full_symbol': 'C12/m1', 'int_number': 12, 'order': 8, 'patterson_symmetry': 'C12/m1', 'point_group': '2/m'}, 'C121': {'enc': '02aDDOcOOO0', 'full_symbol': 'C121', 'int_number': 5, 'order': 4, 'patterson_symmetry': 'C12/m1', 'point_group': '2'}, 'C1c1': {'enc': '02aDDOjOOD0', 'full_symbol': 'C1c1', 'int_number': 9, 'order': 4, 'patterson_symmetry': 'C12/m1', 'point_group': 'm'}, 'C1m1': {'enc': '02aDDOjOOO0', 'full_symbol': 'C1m1', 'int_number': 8, 'order': 4, 'patterson_symmetry': 'C12/m1', 'point_group': 'm'}, 'C222': {'enc': '03aDDObOOOcOOO0', 'full_symbol': 'C222', 'int_number': 21, 'order': 8, 'patterson_symmetry': 'Cmmm', 'point_group': '222'}, 'C222_1': {'enc': '03aDDObOODcOOD0', 'full_symbol': 'C222_1', 'int_number': 20, 'order': 8, 'patterson_symmetry': 'Cmmm', 'point_group': '222'}, 'Ccc2': {'enc': '03aDDObOOOjOOD0', 'full_symbol': 'Ccc2', 'int_number': 37, 'order': 8, 'patterson_symmetry': 'Cmmm', 'point_group': 'mm2'}, 'Ccca': {'enc': '04aDDObDDOcOOOhODD1OBB', 'full_symbol': 'C2/c2/c2/e', 'int_number': 68, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Ccce': {'enc': '04aDDObDDOcOOOhODD1OBB', 'full_symbol': 'C2/c2/c2/e', 'int_number': 68, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cccm': {'enc': '13aDDObOOOcOOD0', 'full_symbol': 'C2/c2/c2/m', 'int_number': 66, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cmc2_1': {'enc': '03aDDObOODjOOD0', 'full_symbol': 'Cmc2_1', 'int_number': 36, 'order': 8, 'patterson_symmetry': 'Cmmm', 'point_group': 'mm2'}, 'Cmce': {'enc': '13aDDObODDcODD0', 'full_symbol': 'C2/m2/c2_1/e', 'int_number': 64, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cmcm': {'enc': '13aDDObOODcOOD0', 'full_symbol': 'C2/m2/c2_1/m', 'int_number': 63, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cmm2': {'enc': '03aDDObOOOjOOO0', 'full_symbol': 'Cmm2', 'int_number': 35, 'order': 8, 'patterson_symmetry': 'Cmmm', 'point_group': 'mm2'}, 'Cmma': {'enc': '13aDDObODOcODO0', 'full_symbol': 'C2/m2/m2/e', 'int_number': 67, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cmme': {'enc': '13aDDObODOcODO0', 'full_symbol': 'C2/m2/m2/e', 'int_number': 67, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'Cmmm': {'enc': '13aDDObOOOcOOO0', 'full_symbol': 'C2/m2/m2/m', 'int_number': 65, 'order': 16, 'patterson_symmetry': 'Cmmm', 'point_group': 'mmm'}, 'F-43c': {'enc': '06aODDaDODbOOOcOOOdOOOlDDD0', 'full_symbol': 'F-43c', 'int_number': 219, 'order': 96, 'patterson_symmetry': 'Fm-3m', 'point_group': '-43m'}, 'F-43m': {'enc': '06aODDaDODbOOOcOOOdOOOlOOO0', 'full_symbol': 'F-43m', 'int_number': 216, 'order': 96, 'patterson_symmetry': 'Fm-3m', 'point_group': '-43m'}, 'F222': {'enc': '04aODDaDODbOOOcOOO0', 'full_symbol': 'F222', 'int_number': 22, 'order': 16, 'patterson_symmetry': 'Fmmm', 'point_group': '222'}, 'F23': {'enc': '05aODDaDODbOOOcOOOdOOO0', 'full_symbol': 'F23', 'int_number': 196, 'order': 48, 'patterson_symmetry': 'Fm-3', 'point_group': '23'}, 'F432': {'enc': '06aODDaDODbOOOcOOOdOOOeOOO0', 'full_symbol': 'F432', 'int_number': 209, 'order': 96, 'patterson_symmetry': 'Fm-3m', 'point_group': '432'}, 'F4_132': {'enc': '06aODDaDODbODDcDDOdOOOeFBF0', 'full_symbol': 'F4_132', 'int_number': 210, 'order': 96, 'patterson_symmetry': 'Fm-3m', 'point_group': '432'}, 'Fd-3': {'enc': '06aODDaDODbOOOcOOOdOOOhBBB1ZZZ', 'full_symbol': 'F2/d-3', 'int_number': 203, 'order': 96, 'patterson_symmetry': 'Fm-3', 'point_group': 'm-3'}, 'Fd-3c': {'enc': '07aODDaDODbODDcDDOdOOOeFBFhFFF1XXX', 'full_symbol': 'F4_1/d-32/c', 'int_number': 228, 'order': 192, 'patterson_symmetry': 'Fm-3m', 'point_group': 'm-3m'}, 'Fd-3m': {'enc': '07aODDaDODbODDcDDOdOOOeFBFhBBB1ZZZ', 'full_symbol': 'F4_1/d-32/m', 'int_number': 227, 'order': 192, 'patterson_symmetry': 'Fm-3m', 'point_group': 'm-3m'}, 'Fdd2': {'enc': '04aODDaDODbOOOjBBB0', 'full_symbol': 'Fdd2', 'int_number': 43, 'order': 16, 'patterson_symmetry': 'Fmmm', 'point_group': 'mm2'}, 'Fddd': {'enc': '05aODDaDODbOOOcOOOhBBB1ZZZ', 'full_symbol': 'F2/d2/d2/d', 'int_number': 70, 'order': 32, 'patterson_symmetry': 'Fmmm', 'point_group': 'mmm'}, 'Fm-3': {'enc': '15aODDaDODbOOOcOOOdOOO0', 'full_symbol': 'F2/m-3', 'int_number': 202, 'order': 96, 'patterson_symmetry': 'Fm-3', 'point_group': 'm-3'}, 'Fm-3c': {'enc': '16aODDaDODbOOOcOOOdOOOeDDD0', 'full_symbol': 'F4/m-32/c', 'int_number': 226, 'order': 192, 'patterson_symmetry': 'Fm-3m', 'point_group': 'm-3m'}, 'Fm-3m': {'enc': '16aODDaDODbOOOcOOOdOOOeOOO0', 'full_symbol': 'F4/m-32/m', 'int_number': 225, 'order': 192, 'patterson_symmetry': 'Fm-3m', 'point_group': 'm-3m'}, 'Fmm2': {'enc': '04aODDaDODbOOOjOOO0', 'full_symbol': 'Fmm2', 'int_number': 42, 'order': 16, 'patterson_symmetry': 'Fmmm', 'point_group': 'mm2'}, 'Fmmm': {'enc': '14aODDaDODbOOOcOOO0', 'full_symbol': 'F2/m2/m2/m', 'int_number': 69, 'order': 32, 'patterson_symmetry': 'Fmmm', 'point_group': 'mmm'}, 'I-4': {'enc': '03aDDDbOOOmOOO0', 'full_symbol': 'I-4', 'int_number': 82, 'order': 8, 'patterson_symmetry': 'I4/m', 'point_group': '-4'}, 'I-42d': {'enc': '04aDDDbOOOmOOOcDOF0', 'full_symbol': 'I-42d', 'int_number': 122, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '-42m'}, 'I-42m': {'enc': '04aDDDbOOOmOOOcOOO0', 'full_symbol': 'I-42m', 'int_number': 121, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '-42m'}, 'I-43d': {'enc': '05aDDDbDODcODDdOOOlBBB0', 'full_symbol': 'I-43d', 'int_number': 220, 'order': 48, 'patterson_symmetry': 'Im-3m', 'point_group': '-43m'}, 'I-43m': {'enc': '05aDDDbOOOcOOOdOOOlOOO0', 'full_symbol': 'I-43m', 'int_number': 217, 'order': 48, 'patterson_symmetry': 'Im-3m', 'point_group': '-43m'}, 'I-4c2': {'enc': '04aDDDbOOOmOOOjOOD0', 'full_symbol': 'I-4c2', 'int_number': 120, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '-42m'}, 'I-4m2': {'enc': '04aDDDbOOOmOOOjOOO0', 'full_symbol': 'I-4m2', 'int_number': 119, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '-42m'}, 'I222': {'enc': '03aDDDbOOOcOOO0', 'full_symbol': 'I222', 'int_number': 23, 'order': 8, 'patterson_symmetry': 'Immm', 'point_group': '222'}, 'I23': {'enc': '04aDDDbOOOcOOOdOOO0', 'full_symbol': 'I23', 'int_number': 197, 'order': 24, 'patterson_symmetry': 'Im-3', 'point_group': '23'}, 'I2_12_12_1': {'enc': '03aDDDbDODcODD0', 'full_symbol': 'I2_12_12_1', 'int_number': 24, 'order': 8, 'patterson_symmetry': 'Immm', 'point_group': '222'}, 'I2_13': {'enc': '04aDDDbDODcODDdOOO0', 'full_symbol': 'I2_13', 'int_number': 199, 'order': 24, 'patterson_symmetry': 'Im-3', 'point_group': '23'}, 'I4': {'enc': '03aDDDbOOOgOOO0', 'full_symbol': 'I4', 'int_number': 79, 'order': 8, 'patterson_symmetry': 'I4/m', 'point_group': '4'}, 'I4/m': {'enc': '13aDDDbOOOgOOO0', 'full_symbol': 'I4/m', 'int_number': 87, 'order': 16, 'patterson_symmetry': 'I4/m', 'point_group': '4/m'}, 'I4/mcm': {'enc': '14aDDDbOOOgOOOcOOD0', 'full_symbol': 'I4/m2/c2/m', 'int_number': 140, 'order': 32, 'patterson_symmetry': 'I4/mmm', 'point_group': '4/mmm'}, 'I4/mmm': {'enc': '14aDDDbOOOgOOOcOOO0', 'full_symbol': 'I4/m2/m2/m', 'int_number': 139, 'order': 32, 'patterson_symmetry': 'I4/mmm', 'point_group': '4/mmm'}, 'I422': {'enc': '04aDDDbOOOgOOOcOOO0', 'full_symbol': 'I422', 'int_number': 97, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '422'}, 'I432': {'enc': '05aDDDbOOOcOOOdOOOeOOO0', 'full_symbol': 'I432', 'int_number': 211, 'order': 48, 'patterson_symmetry': 'Im-3m', 'point_group': '432'}, 'I4_1': {'enc': '03aDDDbDDDgODB0', 'full_symbol': 'I4_1', 'int_number': 80, 'order': 8, 'patterson_symmetry': 'I4/m', 'point_group': '4'}, 'I4_1/a': {'enc': '04aDDDbDDDgODBhODB1OYZ', 'full_symbol': 'I4_1/a', 'int_number': 88, 'order': 16, 'patterson_symmetry': 'I4/m', 'point_group': '4/m'}, 'I4_1/acd': {'enc': '05aDDDbDDDgODBcDOBhODB1OBZ', 'full_symbol': 'I4_1/a2/c2/d', 'int_number': 142, 'order': 32, 'patterson_symmetry': 'I4/mmm', 'point_group': '4/mmm'}, 'I4_1/amd': {'enc': '05aDDDbDDDgODBcDOFhODB1OBZ', 'full_symbol': 'I4_1/a2/m2/d', 'int_number': 141, 'order': 32, 'patterson_symmetry': 'I4/mmm', 'point_group': '4/mmm'}, 'I4_122': {'enc': '04aDDDbDDDgODBcDOF0', 'full_symbol': 'I4_122', 'int_number': 98, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '422'}, 'I4_132': {'enc': '05aDDDbDODcODDdOOOeFBB0', 'full_symbol': 'I4_132', 'int_number': 214, 'order': 48, 'patterson_symmetry': 'Im-3m', 'point_group': '432'}, 'I4_1cd': {'enc': '04aDDDbDDDgODBjOOD0', 'full_symbol': 'I4_1cd', 'int_number': 110, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '4mm'}, 'I4_1md': {'enc': '04aDDDbDDDgODBjOOO0', 'full_symbol': 'I4_1md', 'int_number': 109, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '4mm'}, 'I4cm': {'enc': '04aDDDbOOOgOOOjOOD0', 'full_symbol': 'I4cm', 'int_number': 108, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '4mm'}, 'I4mm': {'enc': '04aDDDbOOOgOOOjOOO0', 'full_symbol': 'I4mm', 'int_number': 107, 'order': 16, 'patterson_symmetry': 'I4/mmm', 'point_group': '4mm'}, 'Ia-3': {'enc': '14aDDDbDODcODDdOOO0', 'full_symbol': 'I2_1/a-3', 'int_number': 206, 'order': 48, 'patterson_symmetry': 'Im-3', 'point_group': 'm-3'}, 'Ia-3d': {'enc': '15aDDDbDODcODDdOOOeFBB0', 'full_symbol': 'I4_1/a-32/d', 'int_number': 230, 'order': 96, 'patterson_symmetry': 'Im-3m', 'point_group': 'm-3m'}, 'Iba2': {'enc': '03aDDDbOOOjDDO0', 'full_symbol': 'Iba2', 'int_number': 45, 'order': 8, 'patterson_symmetry': 'Immm', 'point_group': 'mm2'}, 'Ibam': {'enc': '13aDDDbOOOcDDO0', 'full_symbol': 'I2/b2/a2/m', 'int_number': 72, 'order': 16, 'patterson_symmetry': 'Immm', 'point_group': 'mmm'}, 'Ibca': {'enc': '13aDDDbDODcODD0', 'full_symbol': 'I2_1/b2_1/c2_1/a', 'int_number': 73, 'order': 16, 'patterson_symmetry': 'Immm', 'point_group': 'mmm'}, 'Im-3': {'enc': '14aDDDbOOOcOOOdOOO0', 'full_symbol': 'I2/m-3', 'int_number': 204, 'order': 48, 'patterson_symmetry': 'Im-3', 'point_group': 'm-3'}, 'Im-3m': {'enc': '15aDDDbOOOcOOOdOOOeOOO0', 'full_symbol': 'I4/m-32/m', 'int_number': 229, 'order': 96, 'patterson_symmetry': 'Im-3m', 'point_group': 'm-3m'}, 'Ima2': {'enc': '03aDDDbOOOjDOO0', 'full_symbol': 'Ima2', 'int_number': 46, 'order': 8, 'patterson_symmetry': 'Immm', 'point_group': 'mm2'}, 'Imm2': {'enc': '03aDDDbOOOjOOO0', 'full_symbol': 'Imm2', 'int_number': 44, 'order': 8, 'patterson_symmetry': 'Immm', 'point_group': 'mm2'}, 'Imma': {'enc': '13aDDDbODOcODO0', 'full_symbol': 'I2_1/m2_1/m2_1/a', 'int_number': 74, 'order': 16, 'patterson_symmetry': 'Immm', 'point_group': 'mmm'}, 'Immm': {'enc': '13aDDDbOOOcOOO0', 'full_symbol': 'I2/m2/m2/m', 'int_number': 71, 'order': 16, 'patterson_symmetry': 'Immm', 'point_group': 'mmm'}, 'P-1': {'enc': '100', 'full_symbol': 'P-1', 'int_number': 2, 'order': 2, 'patterson_symmetry': 'P-1', 'point_group': '-1'}, 'P-3': {'enc': '11nOOO0', 'full_symbol': 'P-3', 'int_number': 147, 'order': 6, 'patterson_symmetry': 'P-3', 'point_group': '-3'}, 'P-31c': {'enc': '12nOOOfOOD0', 'full_symbol': 'P-312/c', 'int_number': 163, 'order': 12, 'patterson_symmetry': 'P-31m', 'point_group': '-3m'}, 'P-31m': {'enc': '12nOOOfOOO0', 'full_symbol': 'P-312/m', 'int_number': 162, 'order': 12, 'patterson_symmetry': 'P-31m', 'point_group': '-3m'}, 'P-3c1': {'enc': '12nOOOeOOD0', 'full_symbol': 'P-32/c1', 'int_number': 165, 'order': 12, 'patterson_symmetry': 'P-3m1', 'point_group': '-3m'}, 'P-3m1': {'enc': '12nOOOeOOO0', 'full_symbol': 'P-32/m1', 'int_number': 164, 'order': 12, 'patterson_symmetry': 'P-3m1', 'point_group': '-3m'}, 'P-4': {'enc': '02bOOOmOOO0', 'full_symbol': 'P-4', 'int_number': 81, 'order': 4, 'patterson_symmetry': 'P4/m', 'point_group': '-4'}, 'P-42_1c': {'enc': '03bOOOmOOOcDDD0', 'full_symbol': 'P-42_1c', 'int_number': 114, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-42_1m': {'enc': '03bOOOmOOOcDDO0', 'full_symbol': 'P-42_1m', 'int_number': 113, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-42c': {'enc': '03bOOOmOOOcOOD0', 'full_symbol': 'P-42c', 'int_number': 112, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-42m': {'enc': '03bOOOmOOOcOOO0', 'full_symbol': 'P-42m', 'int_number': 111, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-43m': {'enc': '04bOOOcOOOdOOOlOOO0', 'full_symbol': 'P-43m', 'int_number': 215, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '-43m'}, 'P-43n': {'enc': '04bOOOcOOOdOOOlDDD0', 'full_symbol': 'P-43n', 'int_number': 218, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '-43m'}, 'P-4b2': {'enc': '03bOOOmOOOjDDO0', 'full_symbol': 'P-4b2', 'int_number': 117, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-4c2': {'enc': '03bOOOmOOOjOOD0', 'full_symbol': 'P-4c2', 'int_number': 116, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-4m2': {'enc': '03bOOOmOOOjOOO0', 'full_symbol': 'P-4m2', 'int_number': 115, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-4n2': {'enc': '03bOOOmOOOjDDD0', 'full_symbol': 'P-4n2', 'int_number': 118, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '-42m'}, 'P-6': {'enc': '02nOOOiOOO0', 'full_symbol': 'P-6', 'int_number': 174, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '-6'}, 'P-62c': {'enc': '03nOOOiOODeOOO0', 'full_symbol': 'P-62c', 'int_number': 190, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '-6m2'}, 'P-62m': {'enc': '03nOOOiOOOeOOO0', 'full_symbol': 'P-62m', 'int_number': 189, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '-6m2'}, 'P-6c2': {'enc': '03nOOOiOODkOOD0', 'full_symbol': 'P-6c2', 'int_number': 188, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '-6m2'}, 'P-6m2': {'enc': '03nOOOiOOOkOOO0', 'full_symbol': 'P-6m2', 'int_number': 187, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '-6m2'}, 'P1': {'enc': '000', 'full_symbol': 'P1', 'int_number': 1, 'order': 1, 'patterson_symmetry': 'P-1', 'point_group': '1'}, 'P12/c1': {'enc': '11cOOD0', 'full_symbol': 'P12/c1', 'int_number': 13, 'order': 4, 'patterson_symmetry': 'P12/m1', 'point_group': '2/m'}, 'P12/m1': {'enc': '11cOOO0', 'full_symbol': 'P12/m1', 'int_number': 10, 'order': 4, 'patterson_symmetry': 'P12/m1', 'point_group': '2/m'}, 'P121': {'enc': '01cOOO0', 'full_symbol': 'P121', 'int_number': 3, 'order': 2, 'patterson_symmetry': 'P12/m1', 'point_group': '2'}, 'P12_1/c1': {'enc': '11cODD0', 'full_symbol': 'P12_1/c1', 'int_number': 14, 'order': 4, 'patterson_symmetry': 'P12/m1', 'point_group': '2/m'}, 'P12_1/m1': {'enc': '11cODO0', 'full_symbol': 'P12_1/m1', 'int_number': 11, 'order': 4, 'patterson_symmetry': 'P12/m1', 'point_group': '2/m'}, 'P12_11': {'enc': '01cODO0', 'full_symbol': 'P12_11', 'int_number': 4, 'order': 2, 'patterson_symmetry': 'P12/m1', 'point_group': '2'}, 'P1c1': {'enc': '01jOOD0', 'full_symbol': 'P1c1', 'int_number': 7, 'order': 2, 'patterson_symmetry': 'P12/m1', 'point_group': 'm'}, 'P1m1': {'enc': '01jOOO0', 'full_symbol': 'P1m1', 'int_number': 6, 'order': 2, 'patterson_symmetry': 'P12/m1', 'point_group': 'm'}, 'P222': {'enc': '02bOOOcOOO0', 'full_symbol': 'P222', 'int_number': 16, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': '222'}, 'P222_1': {'enc': '02bOODcOOD0', 'full_symbol': 'P222_1', 'int_number': 17, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': '222'}, 'P23': {'enc': '03bOOOcOOOdOOO0', 'full_symbol': 'P23', 'int_number': 195, 'order': 12, 'patterson_symmetry': 'Pm-3', 'point_group': '23'}, 'P2_12_12': {'enc': '02bOOOcDDO0', 'full_symbol': 'P2_12_12', 'int_number': 18, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': '222'}, 'P2_12_12_1': {'enc': '02bDODcODD0', 'full_symbol': 'P2_12_12_1', 'int_number': 19, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': '222'}, 'P2_13': {'enc': '03bDODcODDdOOO0', 'full_symbol': 'P2_13', 'int_number': 198, 'order': 12, 'patterson_symmetry': 'Pm-3', 'point_group': '23'}, 'P3': {'enc': '01nOOO0', 'full_symbol': 'P3', 'int_number': 143, 'order': 3, 'patterson_symmetry': 'P-3', 'point_group': '3'}, 'P312': {'enc': '02nOOOfOOO0', 'full_symbol': 'P312', 'int_number': 149, 'order': 6, 'patterson_symmetry': 'P-31m', 'point_group': '32'}, 'P31c': {'enc': '02nOOOlOOD0', 'full_symbol': 'P31c', 'int_number': 159, 'order': 6, 'patterson_symmetry': 'P-31m', 'point_group': '3m'}, 'P31m': {'enc': '02nOOOlOOO0', 'full_symbol': 'P31m', 'int_number': 157, 'order': 6, 'patterson_symmetry': 'P-31m', 'point_group': '3m'}, 'P321': {'enc': '02nOOOeOOO0', 'full_symbol': 'P321', 'int_number': 150, 'order': 6, 'patterson_symmetry': 'P-3m1', 'point_group': '32'}, 'P3_1': {'enc': '01nOOC0', 'full_symbol': 'P3_1', 'int_number': 144, 'order': 3, 'patterson_symmetry': 'P-3', 'point_group': '3'}, 'P3_112': {'enc': '02nOOCfOOE0', 'full_symbol': 'P3_112', 'int_number': 151, 'order': 6, 'patterson_symmetry': 'P-31m', 'point_group': '32'}, 'P3_121': {'enc': '02nOOCeOOO0', 'full_symbol': 'P3_121', 'int_number': 152, 'order': 6, 'patterson_symmetry': 'P-3m1', 'point_group': '32'}, 'P3_2': {'enc': '01nOOE0', 'full_symbol': 'P3_2', 'int_number': 145, 'order': 3, 'patterson_symmetry': 'P-3', 'point_group': '3'}, 'P3_212': {'enc': '02nOOEfOOC0', 'full_symbol': 'P3_212', 'int_number': 153, 'order': 6, 'patterson_symmetry': 'P-31m', 'point_group': '32'}, 'P3_221': {'enc': '02nOOEeOOO0', 'full_symbol': 'P3_221', 'int_number': 154, 'order': 6, 'patterson_symmetry': 'P-3m1', 'point_group': '32'}, 'P3c1': {'enc': '02nOOOkOOD0', 'full_symbol': 'P3c1', 'int_number': 158, 'order': 6, 'patterson_symmetry': 'P-3m1', 'point_group': '3m'}, 'P3m1': {'enc': '02nOOOkOOO0', 'full_symbol': 'P3m1', 'int_number': 156, 'order': 6, 'patterson_symmetry': 'P-3m1', 'point_group': '3m'}, 'P4': {'enc': '02bOOOgOOO0', 'full_symbol': 'P4', 'int_number': 75, 'order': 4, 'patterson_symmetry': 'P4/m', 'point_group': '4'}, 'P4/m': {'enc': '12bOOOgOOO0', 'full_symbol': 'P4/m', 'int_number': 83, 'order': 8, 'patterson_symmetry': 'P4/m', 'point_group': '4/m'}, 'P4/mbm': {'enc': '13bOOOgOOOcDDO0', 'full_symbol': 'P4/m2_1/b2/m', 'int_number': 127, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/mcc': {'enc': '13bOOOgOOOcOOD0', 'full_symbol': 'P4/m2/c2/c', 'int_number': 124, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/mmm': {'enc': '13bOOOgOOOcOOO0', 'full_symbol': 'P4/m2/m2/m', 'int_number': 123, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/mnc': {'enc': '13bOOOgOOOcDDD0', 'full_symbol': 'P4/m2_1/n2/c', 'int_number': 128, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/n': {'enc': '03bOOOgDDOhDDO1YBO', 'full_symbol': 'P4/n', 'int_number': 85, 'order': 8, 'patterson_symmetry': 'P4/m', 'point_group': '4/m'}, 'P4/nbm': {'enc': '04bOOOgOOOcOOOhDDO1YYO', 'full_symbol': 'P4/n2/b2/m', 'int_number': 125, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/ncc': {'enc': '04bOOOgDDOcDDDhDDO1YBO', 'full_symbol': 'P4/n2_1/c2/c', 'int_number': 130, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/nmm': {'enc': '04bOOOgDDOcDDOhDDO1YBO', 'full_symbol': 'P4/n2_1/m2/m', 'int_number': 129, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4/nnc': {'enc': '04bOOOgOOOcOOOhDDD1YYY', 'full_symbol': 'P4/n2/n2/c', 'int_number': 126, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P422': {'enc': '03bOOOgOOOcOOO0', 'full_symbol': 'P422', 'int_number': 89, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P42_12': {'enc': '03bOOOgDDOcDDO0', 'full_symbol': 'P42_12', 'int_number': 90, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P432': {'enc': '04bOOOcOOOdOOOeOOO0', 'full_symbol': 'P432', 'int_number': 207, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '432'}, 'P4_1': {'enc': '02bOODgOOB0', 'full_symbol': 'P4_1', 'int_number': 76, 'order': 4, 'patterson_symmetry': 'P4/m', 'point_group': '4'}, 'P4_122': {'enc': '03bOODgOOBcOOO0', 'full_symbol': 'P4_122', 'int_number': 91, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_12_12': {'enc': '03bOODgDDBcDDB0', 'full_symbol': 'P4_12_12', 'int_number': 92, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_132': {'enc': '04bDODcODDdOOOeFBB0', 'full_symbol': 'P4_132', 'int_number': 213, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '432'}, 'P4_2': {'enc': '02bOOOgOOD0', 'full_symbol': 'P4_2', 'int_number': 77, 'order': 4, 'patterson_symmetry': 'P4/m', 'point_group': '4'}, 'P4_2/m': {'enc': '12bOOOgOOD0', 'full_symbol': 'P4_2/m', 'int_number': 84, 'order': 8, 'patterson_symmetry': 'P4/m', 'point_group': '4/m'}, 'P4_2/mbc': {'enc': '13bOOOgOODcDDO0', 'full_symbol': 'P4_2/m2_1/b2/c', 'int_number': 135, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/mcm': {'enc': '13bOOOgOODcOOD0', 'full_symbol': 'P4_2/m2/c2/m', 'int_number': 132, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/mmc': {'enc': '13bOOOgOODcOOO0', 'full_symbol': 'P4_2/m2/m2/c', 'int_number': 131, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/mnm': {'enc': '13bOOOgDDDcDDD0', 'full_symbol': 'P4_2/m2_1/n2/m', 'int_number': 136, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/n': {'enc': '03bOOOgDDDhDDD1YYY', 'full_symbol': 'P4_2/n', 'int_number': 86, 'order': 8, 'patterson_symmetry': 'P4/m', 'point_group': '4/m'}, 'P4_2/nbc': {'enc': '04bOOOgDDDcOODhDDD1YBY', 'full_symbol': 'P4_2/n2/b2/c', 'int_number': 133, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/ncm': {'enc': '04bOOOgDDDcDDOhDDD1YBY', 'full_symbol': 'P4_2/n2_1/c2/m', 'int_number': 138, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/nmc': {'enc': '04bOOOgDDDcDDDhDDD1YBY', 'full_symbol': 'P4_2/n2_1/m2/c', 'int_number': 137, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_2/nnm': {'enc': '04bOOOgDDDcOOOhDDD1YBY', 'full_symbol': 'P4_2/n2/n2/m', 'int_number': 134, 'order': 16, 'patterson_symmetry': 'P4/mmm', 'point_group': '4/mmm'}, 'P4_222': {'enc': '03bOOOgOODcOOO0', 'full_symbol': 'P4_222', 'int_number': 93, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_22_12': {'enc': '03bOOOgDDDcDDD0', 'full_symbol': 'P4_22_12', 'int_number': 94, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_232': {'enc': '04bOOOcOOOdOOOeDDD0', 'full_symbol': 'P4_232', 'int_number': 208, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '432'}, 'P4_2bc': {'enc': '03bOOOgOODjDDO0', 'full_symbol': 'P4_2bc', 'int_number': 106, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4_2cm': {'enc': '03bOOOgOODjOOD0', 'full_symbol': 'P4_2cm', 'int_number': 101, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4_2mc': {'enc': '03bOOOgOODjOOO0', 'full_symbol': 'P4_2mc', 'int_number': 105, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4_2nm': {'enc': '03bOOOgDDDjDDD0', 'full_symbol': 'P4_2nm', 'int_number': 102, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4_3': {'enc': '02bOODgOOF0', 'full_symbol': 'P4_3', 'int_number': 78, 'order': 4, 'patterson_symmetry': 'P4/m', 'point_group': '4'}, 'P4_322': {'enc': '03bOODgOOFcOOO0', 'full_symbol': 'P4_322', 'int_number': 95, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_32_12': {'enc': '03bOODgDDFcDDF0', 'full_symbol': 'P4_32_12', 'int_number': 96, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '422'}, 'P4_332': {'enc': '04bDODcODDdOOOeBFF0', 'full_symbol': 'P4_332', 'int_number': 212, 'order': 24, 'patterson_symmetry': 'Pm-3m', 'point_group': '432'}, 'P4bm': {'enc': '03bOOOgOOOjDDO0', 'full_symbol': 'P4bm', 'int_number': 100, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4cc': {'enc': '03bOOOgOOOjOOD0', 'full_symbol': 'P4cc', 'int_number': 103, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4mm': {'enc': '03bOOOgOOOjOOO0', 'full_symbol': 'P4mm', 'int_number': 99, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P4nc': {'enc': '03bOOOgOOOjDDD0', 'full_symbol': 'P4nc', 'int_number': 104, 'order': 8, 'patterson_symmetry': 'P4/mmm', 'point_group': '4mm'}, 'P6': {'enc': '02nOOObOOO0', 'full_symbol': 'P6', 'int_number': 168, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6/m': {'enc': '12nOOObOOO0', 'full_symbol': 'P6/m', 'int_number': 175, 'order': 12, 'patterson_symmetry': 'P6/m', 'point_group': '6/m'}, 'P6/mcc': {'enc': '13nOOObOOOeOOD0', 'full_symbol': 'P6/m2/c2/c', 'int_number': 192, 'order': 24, 'patterson_symmetry': 'P6/mmm', 'point_group': '6/mmm'}, 'P6/mmm': {'enc': '13nOOObOOOeOOO0', 'full_symbol': 'P6/m2/m2/m', 'int_number': 191, 'order': 24, 'patterson_symmetry': 'P6/mmm', 'point_group': '6/mmm'}, 'P622': {'enc': '03nOOObOOOeOOO0', 'full_symbol': 'P622', 'int_number': 177, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6_1': {'enc': '02nOOCbOOD0', 'full_symbol': 'P6_1', 'int_number': 169, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6_122': {'enc': '03nOOCbOODeOOC0', 'full_symbol': 'P6_122', 'int_number': 178, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6_2': {'enc': '02nOOEbOOO0', 'full_symbol': 'P6_2', 'int_number': 171, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6_222': {'enc': '03nOOEbOOOeOOE0', 'full_symbol': 'P6_222', 'int_number': 180, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6_3': {'enc': '02nOOObOOD0', 'full_symbol': 'P6_3', 'int_number': 173, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6_3/m': {'enc': '12nOOObOOD0', 'full_symbol': 'P6_3/m', 'int_number': 176, 'order': 12, 'patterson_symmetry': 'P6/m', 'point_group': '6/m'}, 'P6_3/mcm': {'enc': '13nOOObOODeOOD0', 'full_symbol': 'P6_3/m2/c2/m', 'int_number': 193, 'order': 24, 'patterson_symmetry': 'P6/mmm', 'point_group': '6/mmm'}, 'P6_3/mmc': {'enc': '13nOOObOODeOOO0', 'full_symbol': 'P6_3/m2/m2/c', 'int_number': 194, 'order': 24, 'patterson_symmetry': 'P6/mmm', 'point_group': '6/mmm'}, 'P6_322': {'enc': '03nOOObOODeOOO0', 'full_symbol': 'P6_322', 'int_number': 182, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6_3cm': {'enc': '03nOOObOODkOOD0', 'full_symbol': 'P6_3cm', 'int_number': 185, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '6mm'}, 'P6_3mc': {'enc': '03nOOObOODkOOO0', 'full_symbol': 'P6_3mc', 'int_number': 186, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '6mm'}, 'P6_4': {'enc': '02nOOCbOOO0', 'full_symbol': 'P6_4', 'int_number': 172, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6_422': {'enc': '03nOOCbOOOeOOC0', 'full_symbol': 'P6_422', 'int_number': 181, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6_5': {'enc': '02nOOEbOOD0', 'full_symbol': 'P6_5', 'int_number': 170, 'order': 6, 'patterson_symmetry': 'P6/m', 'point_group': '6'}, 'P6_522': {'enc': '03nOOEbOODeOOE0', 'full_symbol': 'P6_522', 'int_number': 179, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '622'}, 'P6cc': {'enc': '03nOOObOOOkOOD0', 'full_symbol': 'P6cc', 'int_number': 184, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '6mm'}, 'P6mm': {'enc': '03nOOObOOOkOOO0', 'full_symbol': 'P6mm', 'int_number': 183, 'order': 12, 'patterson_symmetry': 'P6/mmm', 'point_group': '6mm'}, 'Pa-3': {'enc': '13bDODcODDdOOO0', 'full_symbol': 'P2_1/a-3', 'int_number': 205, 'order': 24, 'patterson_symmetry': 'Pm-3', 'point_group': 'm-3'}, 'Pba2': {'enc': '02bOOOjDDO0', 'full_symbol': 'Pba2', 'int_number': 32, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pbam': {'enc': '12bOOOcDDO0', 'full_symbol': 'P2_1/b2_1/a2/m', 'int_number': 55, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pban': {'enc': '03bOOOcOOOhDDO1BBO', 'full_symbol': 'P2/b2/a2/n', 'int_number': 50, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pbca': {'enc': '12bDODcODD0', 'full_symbol': 'P2_1/b2_1/c2_1/a', 'int_number': 61, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pbcm': {'enc': '12bOODcODD0', 'full_symbol': 'P2/b2_1/c2_1/m', 'int_number': 57, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pbcn': {'enc': '12bDDDcOOD0', 'full_symbol': 'P2_1/b2/c2_1/n', 'int_number': 60, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pca2_1': {'enc': '02bOODjDOO0', 'full_symbol': 'Pca2_1', 'int_number': 29, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pcc2': {'enc': '02bOOOjOOD0', 'full_symbol': 'Pcc2', 'int_number': 27, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pcca': {'enc': '12bDOOcOOD0', 'full_symbol': 'P2_1/c2/c2/a', 'int_number': 54, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pccm': {'enc': '12bOOOcOOD0', 'full_symbol': 'P2/c2/c2/m', 'int_number': 49, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pccn': {'enc': '12bDDOcODD0', 'full_symbol': 'P2_1/c2_1/c2/n', 'int_number': 56, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pm-3': {'enc': '13bOOOcOOOdOOO0', 'full_symbol': 'P2/m-3', 'int_number': 200, 'order': 24, 'patterson_symmetry': 'Pm-3', 'point_group': 'm-3'}, 'Pm-3m': {'enc': '14bOOOcOOOdOOOeOOO0', 'full_symbol': 'P4/m-32/m', 'int_number': 221, 'order': 48, 'patterson_symmetry': 'Pm-3m', 'point_group': 'm-3m'}, 'Pm-3n': {'enc': '14bOOOcOOOdOOOeDDD0', 'full_symbol': 'P4_2/m-32/n', 'int_number': 223, 'order': 48, 'patterson_symmetry': 'Pm-3m', 'point_group': 'm-3m'}, 'Pma2': {'enc': '02bOOOjDOO0', 'full_symbol': 'Pma2', 'int_number': 28, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pmc2_1': {'enc': '02bOODjOOD0', 'full_symbol': 'Pmc2_1', 'int_number': 26, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pmm2': {'enc': '02bOOOjOOO0', 'full_symbol': 'Pmm2', 'int_number': 25, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pmma': {'enc': '12bDOOcOOO0', 'full_symbol': 'P2_1/m2/m2/a', 'int_number': 51, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pmmm': {'enc': '12bOOOcOOO0', 'full_symbol': 'P2/m2/m2/m', 'int_number': 47, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pmmn': {'enc': '03bOOOcDDOhDDO1BBO', 'full_symbol': 'P2_1/m2_1/m2/n', 'int_number': 59, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pmn2_1': {'enc': '02bDODjDOD0', 'full_symbol': 'Pmn2_1', 'int_number': 31, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pmna': {'enc': '12bDODcDOD0', 'full_symbol': 'P2/m2/n2_1/a', 'int_number': 53, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pn-3': {'enc': '04bOOOcOOOdOOOhDDD1YYY', 'full_symbol': 'P2/n-3', 'int_number': 201, 'order': 24, 'patterson_symmetry': 'Pm-3', 'point_group': 'm-3'}, 'Pn-3m': {'enc': '05bOOOcOOOdOOOeDDDhDDD1YYY', 'full_symbol': 'P4_2/n-32/m', 'int_number': 224, 'order': 48, 'patterson_symmetry': 'Pm-3m', 'point_group': 'm-3m'}, 'Pn-3n': {'enc': '05bOOOcOOOdOOOeOOOhDDD1YYY', 'full_symbol': 'P4/n-32/n', 'int_number': 222, 'order': 48, 'patterson_symmetry': 'Pm-3m', 'point_group': 'm-3m'}, 'Pna2_1': {'enc': '02bOODjDDO0', 'full_symbol': 'Pna2_1', 'int_number': 33, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pnc2': {'enc': '02bOOOjODD0', 'full_symbol': 'Pnc2', 'int_number': 30, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pnma': {'enc': '12bDODcODO0', 'full_symbol': 'P2_1/n2_1/m2_1/a', 'int_number': 62, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pnn2': {'enc': '02bOOOjDDD0', 'full_symbol': 'Pnn2', 'int_number': 34, 'order': 4, 'patterson_symmetry': 'Pmmm', 'point_group': 'mm2'}, 'Pnna': {'enc': '12bDOOcDDD0', 'full_symbol': 'P2/n2_1/n2/a', 'int_number': 52, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pnnm': {'enc': '12bOOOcDDD0', 'full_symbol': 'P2_1/n2_1/n2/m', 'int_number': 58, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'Pnnn': {'enc': '03bOOOcOOOhDDD1BBB', 'full_symbol': 'P2/n2/n2/n', 'int_number': 48, 'order': 8, 'patterson_symmetry': 'Pmmm', 'point_group': 'mmm'}, 'R-3': {'enc': '12aECCnOOO0', 'full_symbol': 'R-3', 'int_number': 148, 'order': 18, 'patterson_symmetry': 'R-3', 'point_group': '-3'}, 'R-3c': {'enc': '13aECCnOOOeOOD0', 'full_symbol': 'R-32/c', 'int_number': 167, 'order': 36, 'patterson_symmetry': 'R-3m', 'point_group': '-3m'}, 'R-3m': {'enc': '13aECCnOOOeOOO0', 'full_symbol': 'R-32/m', 'int_number': 166, 'order': 36, 'patterson_symmetry': 'R-3m', 'point_group': '-3m'}, 'R3': {'enc': '02aECCnOOO0', 'full_symbol': 'R3', 'int_number': 146, 'order': 9, 'patterson_symmetry': 'R-3', 'point_group': '3'}, 'R32': {'enc': '03aECCnOOOeOOO0', 'full_symbol': 'R32', 'int_number': 155, 'order': 18, 'patterson_symmetry': 'R-3m', 'point_group': '32'}, 'R3c': {'enc': '03aECCnOOOkOOD0', 'full_symbol': 'R3c', 'int_number': 161, 'order': 18, 'patterson_symmetry': 'R-3m', 'point_group': '3m'}, 'R3m': {'enc': '03aECCnOOOkOOO0', 'full_symbol': 'R3m', 'int_number': 160, 'order': 18, 'patterson_symmetry': 'R-3m', 'point_group': '3m'}}[source]

property symmetry_ops: set[SymmOp][source]

Full set of symmetry operations as matrices. Lazily initialized as generation sometimes takes a bit of time.

to_pretty_string() → str[source]

Returns:

A pretty string representation of the space group.

Return type:

str

translations: ClassVar[dict[str, Fraction]] = {'A': Fraction(1, 6), 'B': Fraction(1, 4), 'C': Fraction(1, 3), 'D': Fraction(1, 2), 'E': Fraction(2, 3), 'F': Fraction(3, 4), 'G': Fraction(5, 6), 'O': Fraction(0, 1), 'X': Fraction(-3, 8), 'Y': Fraction(-1, 4), 'Z': Fraction(-1, 8)}[source]