httk.atomistic.symmetry.spacegroup¶

One identified space-group setting: its symbols, operations, and Wyckoff positions.

A Spacegroup is a setting, not a space-group type. SG 15 has eighteen tabulated settings, and they are genuinely different coordinate systems: Wyckoff letter e is 0,y,1/4 in the reference setting 15:b1 but 1/4,0,z in 15:c1. Everything a Spacegroup exposes — its symmetry operations, its Wyckoff table — is expressed in its own setting’s coordinates.

ASUStructure normally holds its Wyckoff data directly against the tabulated setting it uses. Conversion through SettingTransform is reserved for operations that explicitly require the IT standard setting, or for an own setting that is not tabulated.

Classes¶

Spacegroup

Represent a tabulated space-group setting from the vendored symmetry data.

Functions¶

wyckoff_letter_map(standard, target)

Map standard-setting Wyckoff letters to their names in another setting.

Module Contents¶

class httk.atomistic.symmetry.spacegroup.Spacegroup(record)[source]¶

Represent a tabulated space-group setting from the vendored symmetry data.

Parameters:: record (collections.abc.Mapping[str, Any]) – The read-only vendored mapping describing one space-group setting.

classmethod standard(it_number)[source]¶

Return the IT standard setting for a space-group number.

Parameters:: it_number (int) – The International Tables space-group number.
Returns:: The IT standard setting for it_number.
Return type:: Self

classmethod from_hall_entry(hall_entry)[source]¶

Return the setting named by a normalized Hall symbol.

For example, "-c_2yc" names one setting.

Parameters:: hall_entry (str) – The normalized Hall symbol naming the setting.
Returns:: The corresponding space-group setting.
Return type:: Self

classmethod from_setting(setting_it_nc)[source]¶

Return the setting named by an IT number and coordinate-system code.

For example, "15:c1" names one setting.

Parameters:: setting_it_nc (str) – The IT setting identifier.
Returns:: The corresponding space-group setting.
Return type:: Self

classmethod from_hm_entry(hm_entry)[source]¶

Return the setting named by a Hermann-Mauguin entry.

For example, "C 1 2/c 1" names one setting.

Parameters:: hm_entry (str) – The Hermann-Mauguin symbol naming the setting.
Returns:: The corresponding space-group setting.
Return type:: Self

property record: collections.abc.Mapping[str, Any][source]¶

Return the raw vendored record for fields this class does not model.

Returns:: The source record for this setting.
Return type:: collections.abc.Mapping[str, Any]

property it_number: int[source]¶

Return the International Tables space-group number.

Returns:: The space-group number from 1 through 230.
Return type:: int

property setting: str[source]¶

Return the setting name, such as "15:c1".

Returns:: The IT number and coordinate-system code.
Return type:: str

property hall_entry: str[source]¶

Return the normalized Hall symbol naming the setting unambiguously.

Returns:: The normalized Hall symbol.
Return type:: str

property hall_symbol: str[source]¶

Return the Hall symbol as conventionally written.

Returns:: The conventional Hall symbol.
Return type:: str

property hermann_mauguin: str[source]¶

Return the short Hermann-Mauguin symbol for this setting.

Returns:: The short Hermann-Mauguin symbol.
Return type:: str

property hermann_mauguin_full: str[source]¶

Return the full Hermann-Mauguin symbol for this setting.

Returns:: The full Hermann-Mauguin symbol.
Return type:: str

property crystal_system: str[source]¶

Return the crystal system, such as "monoclinic".

Returns:: The crystal-system name.
Return type:: str

property centring_type: str[source]¶

Return the lattice centring letter, such as "P", "C", or "F".

Returns:: The centring letter.
Return type:: str

property is_standard_setting: bool[source]¶

Report whether this is the IT standard setting for its space-group number.

Returns:: Whether this setting is the IT reference setting.
Return type:: bool

property symmetry_operations: tuple[httk.atomistic.symmetry.affine_operation.AffineOperation, Ellipsis][source]¶

Return every symmetry operation of the group in this setting’s coordinates.

The full set with centring translations already folded in, so its length is the group order and no separate centring pass is needed.

Returns:: The complete tuple of symmetry operations.
Return type:: tuple[httk.atomistic.symmetry.affine_operation.AffineOperation, Ellipsis]

property centering_translations: tuple[httk.core.FracVector, Ellipsis][source]¶

Return the lattice centring translations, including zero.

Returns:: The centring translations in this setting.
Return type:: tuple[httk.core.FracVector, Ellipsis]

property wyckoff: tuple[httk.atomistic.symmetry.wyckoff.WyckoffPosition, Ellipsis][source]¶

Return the Wyckoff positions ordered most specific first.

Sorted by (free_count, multiplicity, letter), so identifying a coordinate by walking this order returns the most specific position it lies on.

Returns:: The ordered Wyckoff positions for this setting.
Return type:: tuple[httk.atomistic.symmetry.wyckoff.WyckoffPosition, Ellipsis]

wyckoff_position(letter)[source]¶

Return the Wyckoff position with the given letter.

For example, "e" selects the position with letter e.

Parameters:: letter (str) – The bare Wyckoff letter.
Returns:: The matching Wyckoff position.
Raises:: KeyError – If this setting has no position with letter.
Return type:: httk.atomistic.symmetry.wyckoff.WyckoffPosition

identify_wyckoff(coordinate)[source]¶

Identify the most specific Wyckoff position holding an exact coordinate.

Returns None when the coordinate lies on no position, which for a complete table means the input was not an exact rational site of this group. Matching is exact: an approximate coordinate must be snapped first (see ASUStructure’s recognition path), never passed here in the hope that it lands.

Parameters:: coordinate (Any) – The exact reduced coordinate to identify.
Returns:: The matching position and free parameters, or None when no position matches exactly.
Return type:: tuple[httk.atomistic.symmetry.wyckoff.WyckoffPosition, httk.core.FracVector] | None

property transform_from_standard: httk.atomistic.symmetry.setting_transform.SettingTransform[source]¶

Return the change of basis from the IT standard setting to this one.

The identity exactly when this is the standard setting.

Returns:: The stored standard-to-own setting transform.
Return type:: httk.atomistic.symmetry.setting_transform.SettingTransform

standard_setting()[source]¶

Return the IT standard setting for this space-group number.

Returns:: The IT standard setting.
Return type:: Spacegroup

httk.atomistic.symmetry.spacegroup.wyckoff_letter_map(standard, target)[source]¶

Map standard-setting Wyckoff letters to their names in another setting.

Almost always the identity — but not always, and the exception is silent. Across all 3210 non-reference (setting, letter) pairs in the vendored tables, exactly one setting permutes letters: in 224:1 the standard setting’s j is that setting’s i and vice versa. So a CIF that declares site 24i in setting 224:1 does not mean standard-setting letter i, and taking the letter at face value across a setting boundary produces the wrong structure with no error.

Computed rather than hard-coded, so it survives a data refresh: each standard position is evaluated at generic parameters, mapped through the setting transform, and identified in the target’s own Wyckoff table.

Parameters:

standard (Spacegroup) – The IT standard setting whose letters are being mapped.
target (Spacegroup) – The setting receiving the mapped letters.

Returns:

A mapping from standard-setting letters to target-setting letters.

Raises:

ValueError – If the settings belong to different space groups or the mapping is not bijective.

Return type:

dict[str, str]