sumo.symmetry package¶

Module contents¶

Package containing functions for symmetry and k-point paths.

Submodules¶

sumo.symmetry.kpoints module¶

Module providing helper functions for generating k-points along a path.

sumo.symmetry.kpoints.get_path_data(structure, mode='bradcrack', symprec=0.01, spg=None, line_density=60, cart_coords=False, kpt_list=None, labels=None, phonopy=False)[source]¶

Get the k-point path, coordinates and symmetry labels for a structure.

If a manual list of kpoints is supplied using the kpt_list variable, the mode option will be ignored.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Parameters:

structure (Structure) – The structure.
mode (str, optional) –
Method used for calculating the high-symmetry path. The options are:

bradcrack
Use the paths from Bradley and Cracknell. See [brad].

pymatgen
Use the paths from pymatgen. See [curt].

latimer-munro
Use the paths from Latimer & Munro. See [lm].

seekpath
Use the paths from SeeK-path. See [seek].
symprec (float, optional) – The tolerance for determining the crystal symmetry.
spg (SpaceGroup, optional) – Space group used to override the symmetry determined by spglib. This is not recommended and only provided for testing purposes. This option will only take effect when mode = 'bradcrack'.
line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
kpt_list (list, optional) –
List of k-points to use, formatted as a list of subpaths, each containing a list of fractional k-points. For example:
```
[ [[0., 0., 0.], [0., 0., 0.5]],
  [[0.5, 0., 0.], [0.5, 0.5, 0.]] ]
```
Will return points along 0 0 0 -> 0 0 1/2 | 1/2 0 0 -> 1/2 1/2 0
path_labels (list, optional) –
The k-point labels. These should be provided as a list of str for each subpath of the overall path. For example:
```
[ ['Gamma', 'Z'], ['X', 'M'] ]
```
combined with the above example for kpt_list would indicate the path: Gamma -> Z | X -> M. If no labels are provided, letters from A -> Z will be used instead.
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of a kpath object, the k-points along the high-symmetry path, and the k-point labels. Returned as (kpath, kpoints, labels).

The type of kpath object will depend on the value of mode and whether kpt_list is set.

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point
coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
[0.5, 0, 0.5]]
labels is a list of the high symmetry labels for
each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray
containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
[[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels.
For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

sumo.symmetry.kpath module¶

Module containing the base class for high-symmetry k-point path determination.

class sumo.symmetry.kpath.Kpath(structure, symprec=0.001)[source]¶

Bases: object

Base class providing helper functions for generating k-point paths.

This class should not be used directly. Instead, one of the BradCrackKpath, SeekpathKpath, or CustomKpath, subclasses should be used.

The main use of this parent object is for standardisation across the differing k-point path generation classes.

Parameters:

structure (Structure) – The structure.
symprec (float, optional) – The tolerance for determining the crystal symmetry.

prim¶

The standardised primitive cell structure for the generated k-point path.

Type:: Structure

conv¶

The standardised conventional cell structure.

Type:: Structure

correct_structure(atol=1e-08)[source]¶

Determine if the structure matches the standard primitive structure.

The standard primitive will be different between seekpath and pymatgen high-symmetry paths, but this is handled by the specific subclasses.

Parameters:: atol (float, optional) – Absolute tolerance used to compare the input structure with the primitive standard structure.
Returns:: True if the structure is the same as the standard primitive, otherwise False.
Return type:: bool

get_kpoints(line_density=20, cart_coords=False, phonopy=False)[source]¶

Return a list of k-points and labels along the high-symmetry path.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Adapted from pymatgen.symmetry.bandstructure.HighSymmKpath.get_kpoints.

Parameters:

line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of the k-points along the high-symmetry path, and k-point labels. Returned as (kpoints, labels).

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
 [0.5, 0, 0.5]]
labels is a list of the high symmetry labels for each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
 [[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels. For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

static get_lattice_type(number)[source]¶

Return the lattice crystal system.

Hexagonal cells are differentiated into rhombohedral and hexagonal lattices.

Parameters:: number (int) – The international space group number.
Returns:: The lattice crystal system.
Return type:: str

property kpoints¶

The high-symmetry k-point labels and their fractional coordinates. Formatted as {label: coords}. For example:

{'\Gamma': [0., 0., 0.], 'X': [0.5, 0. 0.]}

Type:: dict

property lattice_type¶

The Bravais lattice system. Hexagonal cells are separated into rhombohedral and hexagonal lattices.

Type:: str

property path¶

The high-symmetry k-point path. Each subpath is provided as a list. For example, the following covers the path \Gamma -> X -> C | \Gamma -> Y:

[['\Gamma', 'X', 'C'], ['\Gamma', 'Y']].

Type:: list

property path_string¶

The high-symmetry k-point path formatted with arrows and showing disconnections between subpaths. For example:

"X -> Gamma | Y -> Z"

Type:: str

property spg_number¶

The international space group number.

Type:: int

property spg_symbol¶

The international space group symbol.

Type:: str

sumo.symmetry.brad_crack_kpath module¶

Module containing class for generating Bradley and Cracknell k-point paths.

class sumo.symmetry.brad_crack_kpath.BradCrackKpath(structure, symprec=0.001, spg=None)[source]¶

Bases: Kpath

Class to generate k-points along paths from Bradley and Cracknell.

The paths used are based on Brillouin zones depicted in reference [brad].

[brad] (1,2)

“The Mathematical Theory of Symmetry in Solids”, C. J. Bradley and A. P. Cracknell, Clarendon Press, 1972.

These paths represent only one particular route through the Brillouin zone and do not cover every possible path (though they do visit every high-symmetry k-point at least once).

These paths should be used with the correct primitive structure. This structure can be accessed using the prim attribute. Compliance between the provided structure and standardised structure checked using the correct_structure() method.

Parameters:

structure (Structure) – The structure.
symprec (float, optional) – The tolerance for determining the crystal symmetry.
spg (SpaceGroup, optional) – Space group used to override the symmetry determined by spglib. This is not recommended and only provided for testing purposes.

prim¶

The standardised primitive cell structure for the generated k-point path.

Type:: Structure

conv¶

The standardised conventional cell structure.

Type:: Structure

correct_structure(atol=1e-08)¶

Determine if the structure matches the standard primitive structure.

The standard primitive will be different between seekpath and pymatgen high-symmetry paths, but this is handled by the specific subclasses.

Parameters:: atol (float, optional) – Absolute tolerance used to compare the input structure with the primitive standard structure.
Returns:: True if the structure is the same as the standard primitive, otherwise False.
Return type:: bool

get_kpoints(line_density=20, cart_coords=False, phonopy=False)¶

Return a list of k-points and labels along the high-symmetry path.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Adapted from pymatgen.symmetry.bandstructure.HighSymmKpath.get_kpoints.

Parameters:

line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of the k-points along the high-symmetry path, and k-point labels. Returned as (kpoints, labels).

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
 [0.5, 0, 0.5]]
labels is a list of the high symmetry labels for each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
 [[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels. For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

static get_lattice_type(number)¶

Return the lattice crystal system.

Hexagonal cells are differentiated into rhombohedral and hexagonal lattices.

Parameters:: number (int) – The international space group number.
Returns:: The lattice crystal system.
Return type:: str

property kpoints¶

The high-symmetry k-point labels and their fractional coordinates. Formatted as {label: coords}. For example:

{'\Gamma': [0., 0., 0.], 'X': [0.5, 0. 0.]}

Type:: dict

property lattice_type¶

The Bravais lattice system. Hexagonal cells are separated into rhombohedral and hexagonal lattices.

Type:: str

property path¶

The high-symmetry k-point path. Each subpath is provided as a list. For example, the following covers the path \Gamma -> X -> C | \Gamma -> Y:

[['\Gamma', 'X', 'C'], ['\Gamma', 'Y']].

Type:: list

property path_string¶

The high-symmetry k-point path formatted with arrows and showing disconnections between subpaths. For example:

"X -> Gamma | Y -> Z"

Type:: str

property spg_number¶

The international space group number.

Type:: int

property spg_symbol¶

The international space group symbol.

Type:: str

sumo.symmetry.pymatgen_kpath module¶

Module containing class for generating k-points along paths from pymatgen.

class sumo.symmetry.pymatgen_kpath.PymatgenKpath(structure, symprec=0.001)[source]¶

Bases: Kpath

Class to generate k-points along paths from pymatgen.

More detail on the paths generated by can be found in the pymatgen documentation. These paths are based on the work described in reference [curt].

[curt] (1,2)

Setyawan, W., & Curtarolo, S. High-throughput electronic band structure calculations: Challenges and tools, Computational Materials Science, 49, 299-312 (2010). doi: 10.1016/j.commatsci.2010.05.010

These paths should be used with primitive structures that comply with the definition from the paper. This structure can be accessed using the prim attribute and compliance between the provided structure and standardised structure checked using the correct_structure() method.

Parameters:

structure (Structure) – The structure.
symprec (float, optional) – The tolerance for determining the crystal symmetry.

prim¶

The standardised primitive cell structure for the generated k-point path.

Type:: Structure

conv¶

The standardised conventional cell structure.

Type:: Structure

correct_structure(atol=1e-08)¶

Determine if the structure matches the standard primitive structure.

The standard primitive will be different between seekpath and pymatgen high-symmetry paths, but this is handled by the specific subclasses.

Parameters:: atol (float, optional) – Absolute tolerance used to compare the input structure with the primitive standard structure.
Returns:: True if the structure is the same as the standard primitive, otherwise False.
Return type:: bool

get_kpoints(line_density=20, cart_coords=False, phonopy=False)¶

Return a list of k-points and labels along the high-symmetry path.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Adapted from pymatgen.symmetry.bandstructure.HighSymmKpath.get_kpoints.

Parameters:

line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of the k-points along the high-symmetry path, and k-point labels. Returned as (kpoints, labels).

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
 [0.5, 0, 0.5]]
labels is a list of the high symmetry labels for each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
 [[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels. For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

static get_lattice_type(number)¶

Return the lattice crystal system.

Hexagonal cells are differentiated into rhombohedral and hexagonal lattices.

Parameters:: number (int) – The international space group number.
Returns:: The lattice crystal system.
Return type:: str

property kpoints¶

The high-symmetry k-point labels and their fractional coordinates. Formatted as {label: coords}. For example:

{'\Gamma': [0., 0., 0.], 'X': [0.5, 0. 0.]}

Type:: dict

property lattice_type¶

The Bravais lattice system. Hexagonal cells are separated into rhombohedral and hexagonal lattices.

Type:: str

property path¶

The high-symmetry k-point path. Each subpath is provided as a list. For example, the following covers the path \Gamma -> X -> C | \Gamma -> Y:

[['\Gamma', 'X', 'C'], ['\Gamma', 'Y']].

Type:: list

property path_string¶

The high-symmetry k-point path formatted with arrows and showing disconnections between subpaths. For example:

"X -> Gamma | Y -> Z"

Type:: str

property spg_number¶

The international space group number.

Type:: int

property spg_symbol¶

The international space group symbol.

Type:: str

sumo.symmetry.seekpath_kpath module¶

Module containing class for generating k-points along paths from SeeK-path.

class sumo.symmetry.seekpath_kpath.SeekpathKpath(structure, symprec=0.001)[source]¶

Bases: Kpath

Class to generate k-points along paths from SeeK-path.

More detail on the paths generated by SeeK-path can be found in reference [seek].

[seek] (1,2)

Y. Hinuma, G. Pizzi, Y. Kumagai, F. Oba, I. Tanaka, Band structure diagram paths based on crystallography, Comp. Mat. Sci. 128, 140 (2017). doi: 10.1016/j.commatsci.2016.10.015

These paths should be used with primitive structures that comply with the definition from the paper. This structure can be accessed using the prim attribute and compliance between the provided structure and standardised structure checked using the correct_structure() method.

Parameters:

structure (Structure) – The structure.
symprec (float, optional) – The tolerance for determining the crystal symmetry.

prim¶

The standardised primitive cell structure for the generated k-point path.

Type:: Structure

conv¶

The standardised conventional cell structure.

Type:: Structure

correct_structure(atol=1e-08)¶

Determine if the structure matches the standard primitive structure.

The standard primitive will be different between seekpath and pymatgen high-symmetry paths, but this is handled by the specific subclasses.

Parameters:: atol (float, optional) – Absolute tolerance used to compare the input structure with the primitive standard structure.
Returns:: True if the structure is the same as the standard primitive, otherwise False.
Return type:: bool

get_kpoints(line_density=20, cart_coords=False, phonopy=False)¶

Return a list of k-points and labels along the high-symmetry path.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Adapted from pymatgen.symmetry.bandstructure.HighSymmKpath.get_kpoints.

Parameters:

line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of the k-points along the high-symmetry path, and k-point labels. Returned as (kpoints, labels).

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
 [0.5, 0, 0.5]]
labels is a list of the high symmetry labels for each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
 [[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels. For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

static get_lattice_type(number)¶

Return the lattice crystal system.

Hexagonal cells are differentiated into rhombohedral and hexagonal lattices.

Parameters:: number (int) – The international space group number.
Returns:: The lattice crystal system.
Return type:: str

classmethod kpath_from_seekpath(seekpath, point_coords)[source]¶

Convert seekpath-formatted kpoints path to sumo-preferred format.

If ‘GAMMA’ is used as a label this will be replaced by ‘Gamma’.

Parameters:

seekpath (list) –
A list of 2-tuples containing the labels at each side of each segment of the k-point path:
```
[(A, B), (B, C), (C, D), ...]
```
where a break in the sequence is indicated by a non-repeating label. E.g.:
```
[(A, B), (B, C), (D, E), ...]
```
for a break between C and D.
point_coords (dict) –
Dict of coordinates corresponding to k-point labels:
```
{'GAMMA': [0., 0., 0.], ...}
```

Returns:

The path and k-points as:

{
    'path', [[l1, l2, l3], [l4, l5], ...],
    'kpoints', {l1: [a1, b1, c1], l2: [a2, b2, c2], ...}
}

Return type:

dict

property kpoints¶

The high-symmetry k-point labels and their fractional coordinates. Formatted as {label: coords}. For example:

{'\Gamma': [0., 0., 0.], 'X': [0.5, 0. 0.]}

Type:: dict

property lattice_type¶

The Bravais lattice system. Hexagonal cells are separated into rhombohedral and hexagonal lattices.

Type:: str

property path¶

The high-symmetry k-point path. Each subpath is provided as a list. For example, the following covers the path \Gamma -> X -> C | \Gamma -> Y:

[['\Gamma', 'X', 'C'], ['\Gamma', 'Y']].

Type:: list

property path_string¶

The high-symmetry k-point path formatted with arrows and showing disconnections between subpaths. For example:

"X -> Gamma | Y -> Z"

Type:: str

property spg_number¶

The international space group number.

Type:: int

property spg_symbol¶

The international space group symbol.

Type:: str

sumo.symmetry.custom_kpath module¶

Module containing class for generating custom k-point paths.

class sumo.symmetry.custom_kpath.CustomKpath(structure, kpt_list, path_labels=None, symprec=0.001)[source]¶

Bases: Kpath

Class to generate k-points along custom k-point paths.

Parameters:

structure (Structure) – The structure.
symprec (float, optional) – The tolerance for determining the crystal symmetry.
kpt_list (list) –
List of k-points to use, formatted as a list of subpaths, each containing a list of fractional k-points. For example:
```
[ [[0., 0., 0.], [0., 0., 0.5]],
  [[0.5, 0., 0.], [0.5, 0.5, 0.]] ]
```
Will return points along 0 0 0 -> 0 0 1/2 | 1/2 0 0 -> 1/2 1/2 0
path_labels (list) –
The k-point labels. These should be provided as a list of str for each subpath of the overall path. For example:
```
[ ['Gamma', 'Z'], ['X', 'M'] ]
```
combined with the above example for kpt_list would indicate the path: Gamma -> Z | X -> M. If no labels are provided, letters from A -> Z will be used instead.

prim¶

The standardised primitive cell structure for the generated k-point path.

Type:: Structure

conv¶

The standardised conventional cell structure.

Type:: Structure

correct_structure(atol=1e-08)¶

Determine if the structure matches the standard primitive structure.

The standard primitive will be different between seekpath and pymatgen high-symmetry paths, but this is handled by the specific subclasses.

Parameters:: atol (float, optional) – Absolute tolerance used to compare the input structure with the primitive standard structure.
Returns:: True if the structure is the same as the standard primitive, otherwise False.
Return type:: bool

get_kpoints(line_density=20, cart_coords=False, phonopy=False)¶

Return a list of k-points and labels along the high-symmetry path.

The format of the returned data will be different if phonopy is True or False. This is because phonopy requires the labels and kpoints to be provided in a different format than kgen.

Adapted from pymatgen.symmetry.bandstructure.HighSymmKpath.get_kpoints.

Parameters:

line_density (int, optional) – Density of k-points along the path.
cart_coords (bool, optional) – Whether the k-points are returned in cartesian or reciprocal coordinates. Defaults to False (fractional coordinates).
phonopy (bool, optional) – Format the k-points and labels for use with phonopy. Defaults to False.

Returns:

A tuple of the k-points along the high-symmetry path, and k-point labels. Returned as (kpoints, labels).

If phonopy == False, then:

kpoints is a numpy.ndarray of the k-point coordinates along the high-symmetry path. For example:
[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0], [0.5, 0, 0.25],
 [0.5, 0, 0.5]]
labels is a list of the high symmetry labels for each k-point (will be an empty str if the k-point has no label). For example:
['\Gamma', '', 'X', '', 'Y']

If phonopy == True, then:

kpoints is a list of numpy.ndarray containing the k-points for each branch of the band structure. This means that the first and last k-points of a particular branch may be repeated. For example:
[[[0, 0, 0], [0.25, 0, 0], [0.5, 0, 0]],
 [[0.5, 0, 0], [0.5, 0, 0.25], [0.5, 0, 0.5]]]
labels is a list of the high symmetry labels. For example:
['\Gamma', 'X', 'Y']

Return type:

tuple

static get_lattice_type(number)¶

Return the lattice crystal system.

Hexagonal cells are differentiated into rhombohedral and hexagonal lattices.

Parameters:: number (int) – The international space group number.
Returns:: The lattice crystal system.
Return type:: str

property kpoints¶

The high-symmetry k-point labels and their fractional coordinates. Formatted as {label: coords}. For example:

{'\Gamma': [0., 0., 0.], 'X': [0.5, 0. 0.]}

Type:: dict

property lattice_type¶

The Bravais lattice system. Hexagonal cells are separated into rhombohedral and hexagonal lattices.

Type:: str

property path¶

The high-symmetry k-point path. Each subpath is provided as a list. For example, the following covers the path \Gamma -> X -> C | \Gamma -> Y:

[['\Gamma', 'X', 'C'], ['\Gamma', 'Y']].

Type:: list

property path_string¶

The high-symmetry k-point path formatted with arrows and showing disconnections between subpaths. For example:

"X -> Gamma | Y -> Z"

Type:: str

property spg_number¶

The international space group number.

Type:: int

property spg_symbol¶

The international space group symbol.

Type:: str