httk property definitionsProperty definitions using the OPTIMADE property definition format, hosted by httk
This page documents an OPTIMADE Property Definition. See https://schemas.optimade.org/ for more information.
ID: https://schemas.httk.org/defs/v0.1/datasets/pointgroups
Definition name: pointgroups
Property name: Point groups
Description: Ordered table of crystallographic point-group records.
Each item contains point-group classification, finite point-group operations, conjugacy classes, and real and complex character tables generated from cctbx and spgrep.
Type: list
Requirements/Conventions:
Examples:
[{"hm_symbol": "2/m", "order": 4}]JSON definition:
{
"$id": "https://schemas.httk.org/defs/v0.1/datasets/pointgroups",
"$schema": "https://schemas.optimade.org/meta/v1.3/optimade/property_definition.json",
"title": "Point groups",
"$comment": "Dataset of pointgroup entries.",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "pointgroups",
"label": "pointgroups_pointgroups"
},
"x-optimade-unit": "inapplicable",
"type": [
"array",
"null"
],
"description": "Ordered table of crystallographic point-group records.\nEach item contains point-group classification, finite point-group operations, conjugacy classes, and real and complex character tables generated from cctbx and spgrep.\n\n**Requirements/Conventions**:\n\n- The table covers the 32 crystallographic point groups.\n- The point-group records are independent of any particular space-group setting.\n- Character-table rows use Mulliken labels and include formatted label variants when available.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/entrytypes/pointgroups",
"x-optimade-type": "dictionary",
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"title": "httk point group symmetry fields",
"x-optimade-definition": {
"kind": "entrytype",
"format": "1.3",
"version": "0.1.0",
"name": "pointgroups",
"label": "pointgroups_entrytype_httk"
},
"properties": {
"id": {
"$id": "https://schemas.optimade.org/defs/v1.2/properties/core/id",
"x-optimade-requirements": {
"support": "must",
"sortable": true,
"query-support": "all mandatory",
"response-level": "always"
},
"title": "ID",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "id_core",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "id"
},
"type": [
"string"
],
"description": "A unique string referencing a specific entry in the database.\n\n**Requirements/Conventions:**\n\n- Taken together, the ID and entry type MUST uniquely identify the entry.\n- Reasonably short IDs are encouraged and SHOULD NOT be longer than 255 characters.\n- IDs MAY change over time.",
"examples": [
"db/1234567",
"cod/2000000",
"cod/2000000@1234567",
"nomad/L1234567890",
"42"
],
"x-optimade-unit": "inapplicable"
},
"type": {
"$id": "https://schemas.optimade.org/defs/v1.2/properties/core/type",
"x-optimade-requirements": {
"support": "must",
"sortable": true,
"query-support": "all mandatory",
"response-level": "always"
},
"title": "type",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "type_core",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "type"
},
"type": [
"string"
],
"description": "The name of the type of an entry.\n\n**Requirements/Conventions:**\n\n- MUST be an existing entry type.\n- The entry of type <type> and ID <id> MUST be returned in response to a request for /<type>/<id> under the versioned or unversioned base URL serving the API.",
"examples": [
"structures"
],
"x-optimade-unit": "inapplicable"
},
"immutable_id": {
"$id": "https://schemas.optimade.org/defs/v1.2/properties/core/immutable_id",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "all mandatory",
"response-level": "may"
},
"title": "immutable ID",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "immutable_id_core",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "immutable_id"
},
"type": [
"string",
"null"
],
"description": "The entry's immutable ID (e.g., a UUID).\n\n**Requirements/Conventions:**\n\n- This is important for databases having preferred IDs that point to \"the latest version\" of a record, but still offer access to older variants.\n- This ID maps to the version-specific record, in case it changes in the future.",
"examples": [
"8bd3e750-b477-41a0-9b11-3a799f21b44f",
"fjeiwoj,54;@=%<>#32"
],
"x-optimade-unit": "inapplicable"
},
"last_modified": {
"$id": "https://schemas.optimade.org/defs/v1.2/properties/core/last_modified",
"x-optimade-requirements": {
"support": "should",
"sortable": false,
"query-support": "all mandatory",
"response-level": "must"
},
"title": "last modified",
"x-optimade-type": "timestamp",
"x-optimade-definition": {
"label": "last_modified_core",
"kind": "property",
"version": "1.2.0",
"format": "1.2",
"name": "last_modified"
},
"type": [
"string",
"null"
],
"format": "date-time",
"description": "Date and time representing when the entry was last modified.",
"examples": [
"2007-04-05T14:30:20Z"
],
"x-optimade-unit": "inapplicable"
},
"character_table_complex": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/character_table_complex",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Complex character table",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "character_table_complex",
"label": "character_table_complex_pointgroups"
},
"type": [
"array",
"null"
],
"description": "Complex irreducible character table of the crystallographic point group.\n\nRows correspond to complex irreducible representations and columns follow the order of `conjugacy_classes`.\nEach character is stored as a dictionary with string fields `re` and `im` representing its real and imaginary components.\nComponents can be integers, rational fractions, or algebraic expressions such as `sqrt(3)/2`; they are not restricted to rational fraction strings.\nFor example, the C3 eigenvalue `exp(2*pi*i/3)` is represented by `re: \"-1/2\"` and `im: \"sqrt(3)/2\"`, preserving its algebraic value without replacing the radical by a decimal approximation.\n\nFor a representation D and class representative g, the character is `trace(D(g))`; every member of a conjugacy class has the same character.\nEach row's character list MUST have length `n_conjugacy_classes`, and its identity-class character MUST equal `dimension`.\nThe number of complex irreducible rows MUST equal `n_conjugacy_classes`, and the sum of their squared dimensions MUST equal `order`.\nThe row inner product is weighted by class size: `sum_C size(C)*conj(chi_a(C))*chi_b(C)/order = delta_ab`.\nConjugate one-dimensional rows use distinct `_a` and `_b` label suffixes even when their `label_markup` renderings coincide; join rows by `label`, not by markup.\nThe current generator places polynomial bases only in `character_table_real`; the optional basis fields retained here are not emitted.\nIn particular, the real two-dimensional span for a conjugate pair must not be interpreted as a basis for either single complex row.",
"x-optimade-unit": "inapplicable",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One row of a point-group character table.",
"properties": {
"label": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Irreducible-representation label.",
"x-optimade-unit": "inapplicable"
},
"label_markup": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/string_markups",
"title": "String markups",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "string_markups",
"label": "string_markups_core"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "Strings with alternate markup and/or encoding for display rendering.\n\nThe object is intended for display-oriented variants only, a sibling property should be used for canonical plain string value.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **html**: OPTIONAL; String.\n HTML rendering of the sibling string, using inline HTML elements where needed for typographic structure such as subscripts, superscripts, overlines, fractions, and line breaks.\n\n - **latex**: OPTIONAL; String.\n LaTeX rendering of the sibling string, suitable for use with a LaTeX or MathJax-like renderer.\n\n - **unicode**: OPTIONAL; String.\n Unicode rendering of the sibling string, using Unicode code points for display features where practical.",
"properties": {
"html": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "HTML rendering of the sibling string."
},
"latex": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "LaTeX rendering of the sibling string."
},
"unicode": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Unicode rendering of the sibling string."
}
},
"examples": [
{
"html": "<i>P</i> 2<sub>1</sub>/<i>c</i>",
"latex": "\\mathit{P}\\,2_{1}/c",
"unicode": "P2\u2081/c"
}
]
},
"dimension": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Dimension of the irreducible representation.",
"x-optimade-unit": "inapplicable"
},
"characters": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Characters for the conjugacy classes in table order.",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One complex character value represented as exact real and imaginary parts.",
"x-optimade-unit": "inapplicable",
"properties": {
"re": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Real component serialized as an integer or rational string for the generated crystallographic tables.",
"x-optimade-unit": "inapplicable"
},
"im": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Imaginary component serialized as a symbolic real-number string, including signed radicals such as `-sqrt(3)/2`; `0` denotes a real character.",
"x-optimade-unit": "inapplicable"
}
}
},
"x-optimade-unit": "inapplicable"
},
"frobenius_schur_indicator": {
"x-optimade-type": "integer",
"enum": [
0,
1,
null
],
"type": [
"integer",
"null"
],
"description": "The complex-irrep indicator `nu = sum_g chi(g^2)/order`.\nThe emitted value 1 means the irrep admits a real realization; 0 means it is of complex type and has a distinct complex-conjugate partner.\nThe crystallographic point groups covered here have no quaternionic-type irreps (whose indicator would be -1).",
"x-optimade-unit": "inapplicable"
},
"basis_linear": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Linear basis polynomials spanning the isotypic component of this representation in the space of linear functions.\nPolynomials use an orthonormal Cartesian frame (x along a, z along c for hexagonal axes) with exact rational coefficients, e.g. `x`, `x+y`.\nThe listed polynomials are linearly independent; repeated copies of a representation are not separated into conventional multiplets.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One basis polynomial in Cartesian x, y, z with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_rotation": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Axial-vector (rotation) basis polynomials spanning the isotypic component of this representation, in the same Cartesian frame as `basis_linear`, e.g. `Rz`, `Rx+Ry`.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One basis polynomial in Rx, Ry, Rz with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_quadratic": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Quadratic basis polynomials spanning the isotypic component of this representation in the space of homogeneous quadratic functions, in the same Cartesian frame as `basis_linear`, e.g. `x^2+y^2`, `x^2-y^2`, `xz`.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One quadratic basis polynomial in x^2, y^2, z^2, xy, xz, yz with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
}
},
"x-optimade-unit": "inapplicable"
},
"examples": [
[
{
"label": "A",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
}
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A",
"unicode": "A"
}
}
],
[
{
"label": "Ag",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
},
{
"re": "1",
"im": "0"
}
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A_{g}",
"unicode": "Ag"
}
},
{
"label": "Au",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
},
{
"re": "-1",
"im": "0"
}
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A_{u}",
"unicode": "Au"
}
}
],
[
{
"label": "A",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
},
{
"re": "1",
"im": "0"
},
{
"re": "1",
"im": "0"
}
],
"frobenius_schur_indicator": 1,
"label_markup": {
"latex": "A",
"unicode": "A"
}
},
{
"label": "E_a",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
},
{
"re": "-1/2",
"im": "sqrt(3)/2"
},
{
"re": "-1/2",
"im": "-sqrt(3)/2"
}
],
"frobenius_schur_indicator": 0,
"label_markup": {
"latex": "E",
"unicode": "E"
}
},
{
"label": "E_b",
"dimension": 1,
"characters": [
{
"re": "1",
"im": "0"
},
{
"re": "-1/2",
"im": "-sqrt(3)/2"
},
{
"re": "-1/2",
"im": "sqrt(3)/2"
}
],
"frobenius_schur_indicator": 0,
"label_markup": {
"latex": "E",
"unicode": "E"
}
}
]
]
},
"character_table_real": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/character_table_real",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Real character table",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "character_table_real",
"label": "character_table_real_pointgroups"
},
"type": [
"array",
"null"
],
"description": "Real irreducible character table of the crystallographic point group.\n\nRows correspond to real irreducible representations and columns follow the order of `conjugacy_classes`.\nCharacters of the real table are exact integers and are therefore stored as plain integers, unlike the symbolic `re`/`im` string pairs of `character_table_complex`.\n\nIrreducibility here is over the real numbers.\nA pair of inequivalent complex-conjugate irreps can combine into one real irrep whose dimension and character are the sums of the constituent dimensions and characters.\nConsequently the number of real rows can be smaller than `n_conjugacy_classes`; such a paired row has character norm two under the class-size-weighted complex character inner product, not one.\nEvery character list MUST follow `conjugacy_classes` and have that list's length, and the identity character MUST equal `dimension`.\nPolynomial bases span each isotypic component, meaning all copies of the indicated real irrep in the chosen polynomial space.\nThe number of listed polynomials can therefore exceed `dimension`, but must be an integer multiple of it.\nLinear and axial spaces each have dimension three; the homogeneous quadratic space has dimension six, including the scalar trace `x^2+y^2+z^2`.\nBasis lists are independent spanning sets, not promised to be orthonormal or partitioned into conventional multiplets; the generator omits a basis field when that irrep is absent from that polynomial space.\nThe coordinates in these polynomial strings are Cartesian variables, unlike the fractional-coordinate variables in `symops`.\nFor a Cartesian operation Q, polar coordinates transform by Q and axial coordinates by `det(Q)*Q`; quadratic polynomials transform by substitution.\nThe final example displays selected A1 and B1 rows of 4mm rather than a complete table; full emitted tables contain every real irrep.",
"x-optimade-unit": "inapplicable",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One row of a point-group character table.",
"properties": {
"label": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Irreducible-representation label.",
"x-optimade-unit": "inapplicable"
},
"label_markup": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/string_markups",
"title": "String markups",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "string_markups",
"label": "string_markups_core"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "Strings with alternate markup and/or encoding for display rendering.\n\nThe object is intended for display-oriented variants only, a sibling property should be used for canonical plain string value.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **html**: OPTIONAL; String.\n HTML rendering of the sibling string, using inline HTML elements where needed for typographic structure such as subscripts, superscripts, overlines, fractions, and line breaks.\n\n - **latex**: OPTIONAL; String.\n LaTeX rendering of the sibling string, suitable for use with a LaTeX or MathJax-like renderer.\n\n - **unicode**: OPTIONAL; String.\n Unicode rendering of the sibling string, using Unicode code points for display features where practical.",
"properties": {
"html": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "HTML rendering of the sibling string."
},
"latex": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "LaTeX rendering of the sibling string."
},
"unicode": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Unicode rendering of the sibling string."
}
},
"examples": [
{
"html": "<i>P</i> 2<sub>1</sub>/<i>c</i>",
"latex": "\\mathit{P}\\,2_{1}/c",
"unicode": "P2\u2081/c"
}
]
},
"dimension": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Dimension of the irreducible representation.",
"x-optimade-unit": "inapplicable"
},
"characters": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Characters for the conjugacy classes in table order.",
"items": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "One real character value represented as an exact integer.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"frobenius_schur_indicator": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Optional Frobenius-Schur annotation; the current generator does not emit this field in the real table.\nThe indicator convention is defined for complex irreducible rows in `character_table_complex`; do not assume a real row formed from a conjugate pair is itself complex-irreducible or has indicator one.",
"x-optimade-unit": "inapplicable"
},
"basis_linear": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Linear basis polynomials spanning the isotypic component of this representation in the space of linear functions.\nPolynomials use an orthonormal Cartesian frame (x along a, z along c for hexagonal axes) with exact rational coefficients, e.g. `x`, `x+y`.\nThe listed polynomials are linearly independent; repeated copies of a representation are not separated into conventional multiplets.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One basis polynomial in Cartesian x, y, z with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_rotation": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Axial-vector (rotation) basis polynomials spanning the isotypic component of this representation, in the same Cartesian frame as `basis_linear`, e.g. `Rz`, `Rx+Ry`.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One basis polynomial in Rx, Ry, Rz with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"basis_quadratic": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Quadratic basis polynomials spanning the isotypic component of this representation in the space of homogeneous quadratic functions, in the same Cartesian frame as `basis_linear`, e.g. `x^2+y^2`, `x^2-y^2`, `xz`.",
"items": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "One quadratic basis polynomial in x^2, y^2, z^2, xy, xz, yz with rational coefficients.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
}
},
"x-optimade-unit": "inapplicable"
},
"examples": [
[
{
"label": "A",
"dimension": 1,
"characters": [
1
],
"basis_linear": [
"x",
"y",
"z"
],
"basis_rotation": [
"Rx",
"Ry",
"Rz"
],
"basis_quadratic": [
"x^2",
"y^2",
"z^2",
"xy",
"xz",
"yz"
],
"label_markup": {
"latex": "A",
"unicode": "A"
}
}
],
[
{
"label": "Ag",
"dimension": 1,
"characters": [
1,
1
],
"basis_rotation": [
"Rx",
"Ry",
"Rz"
],
"basis_quadratic": [
"x^2",
"y^2",
"z^2",
"xy",
"xz",
"yz"
],
"label_markup": {
"latex": "A_{g}",
"unicode": "Ag"
}
},
{
"label": "Au",
"dimension": 1,
"characters": [
1,
-1
],
"basis_linear": [
"x",
"y",
"z"
],
"label_markup": {
"latex": "A_{u}",
"unicode": "Au"
}
}
],
[
{
"label": "A1",
"dimension": 1,
"characters": [
1,
1,
1,
1,
1
],
"basis_linear": [
"z"
],
"basis_quadratic": [
"x^2+y^2",
"z^2"
],
"label_markup": {
"latex": "A_{1}",
"unicode": "A\u2081"
}
},
{
"label": "B1",
"dimension": 1,
"characters": [
1,
1,
-1,
1,
-1
],
"basis_quadratic": [
"x^2-y^2"
],
"label_markup": {
"latex": "B_{1}",
"unicode": "B\u2081"
}
}
]
]
},
"conjugacy_classes": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/conjugacy_classes",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Conjugacy classes",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "conjugacy_classes",
"label": "conjugacy_classes_pointgroups"
},
"type": [
"array",
"null"
],
"description": "Conjugacy classes of a crystallographic point group.\n\nEach class lists its member operation indices, a representative operation, a conventional class label, and operation-type metadata used by the character tables.\nOperation indices refer to positions in the `symops` list of the same point-group record, starting at 0.\n\n**Requirements/Conventions**:\n\n- It MUST be a list of dictionaries, one per conjugacy class, ordered consistently with the character tables.\n- **size** MUST equal the length of **members**.\n- **op\\_type** is the signed integer rotation-type code of the representative operation: `1`, `2`, `3`, `4`, `6` for proper rotations, and the negated value for the corresponding rotoinversions, with `-2` denoting a mirror plane.\n\nTwo operations g and h belong to the same class precisely when `h = a*g*a^-1` for an operation a of this point group.\nThe `members` lists MUST partition the indices of `symops`, and `representative` MUST be a member of its class.\nClass sizes therefore sum to `order`.\nThe class order defines character-table columns and must not be changed without applying the same permutation to every character row.\nClass labels use Schoenflies-style rotation-reflection notation: `S_n` combines a rotation through `2*pi/n` with reflection perpendicular to its axis.\nFor odd n the order of `S_n` is `2*n`, so its inverse is `S_n^(2*n-1)`; these powers must not be confused with crystallographic rotoinversion type codes in `op_type`.\nThe reported `op_axis` follows the same direct-lattice direction convention as `symops[representative].axis`; labels are display aids, while the operation matrix fixes the action.",
"x-optimade-unit": "inapplicable",
"items": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "One conjugacy class of a crystallographic point group.",
"properties": {
"label": {
"x-optimade-type": "dictionary",
"type": [
"object",
"null"
],
"description": "Rendered class label.",
"properties": {
"ascii": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Plain-text rendering intended for logs, command-line output, or compact display.",
"x-optimade-unit": "inapplicable"
},
"unicode": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "Unicode rendering of the same label.",
"x-optimade-unit": "inapplicable"
},
"latex": {
"x-optimade-type": "string",
"type": [
"string",
"null"
],
"description": "LaTeX rendering of the same label.",
"x-optimade-unit": "inapplicable"
}
},
"x-optimade-unit": "inapplicable"
},
"size": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Number of point-group operations in the class. It MUST equal the length of `members`.",
"x-optimade-unit": "inapplicable"
},
"members": {
"x-optimade-type": "list",
"type": [
"array",
"null"
],
"description": "Indices into the `symops` list of the operations belonging to this class.",
"items": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Operation index into `symops`.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
},
"representative": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Index into `symops` of a representative operation for the class.",
"x-optimade-unit": "inapplicable"
},
"op_type": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "Signed integer rotation-type code of the representative operation; negative values denote rotoinversions, with `-2` denoting a mirror plane.",
"enum": [
1,
-1,
2,
-2,
3,
-3,
4,
-4,
6,
-6,
null
],
"x-optimade-unit": "inapplicable"
},
"op_axis": {
"x-optimade-type": "list",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Integer-vector axis or invariant direction of the representative operation; `[0, 0, 0]` when no axis is applicable.",
"items": {
"x-optimade-type": "integer",
"type": [
"integer",
"null"
],
"description": "One integer component of the axis vector.",
"x-optimade-unit": "inapplicable"
},
"x-optimade-unit": "inapplicable"
}
},
"x-optimade-unit": "inapplicable"
},
"examples": [
[
{
"label": {
"ascii": "E",
"unicode": "E",
"latex": "E"
},
"size": 1,
"members": [
0
],
"representative": 0,
"op_type": 1,
"op_axis": [
0,
0,
0
]
},
{
"label": {
"ascii": "i",
"unicode": "i",
"latex": "i"
},
"size": 1,
"members": [
1
],
"representative": 1,
"op_type": -1,
"op_axis": [
0,
0,
0
]
}
]
]
},
"crystal_system": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/crystal_system",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Crystal system",
"x-optimade-type": "string",
"x-compatibility": [
"https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group.crystal_system.html"
],
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "crystal_system",
"label": "crystal_system_pointgroups"
},
"type": [
"string",
"null"
],
"description": "The crystal system of the space group or point group.\n\nValues use the conventional crystallographic system names.\n\nThis classifies the crystallographic point symmetry, not a measured set of lattice lengths and angles.\nTrigonal groups remain trigonal whether described in hexagonal or rhombohedral axes; use `bravais_type` on a space-group record for the translational lattice type.\nNull denotes unavailable classification, not an additional crystal system.",
"x-optimade-unit": "inapplicable",
"enum": [
"triclinic",
"monoclinic",
"orthorhombic",
"tetragonal",
"trigonal",
"hexagonal",
"cubic",
null
],
"examples": [
"triclinic",
"monoclinic"
]
},
"hm_symbol": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/hm_symbol",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Hermann-Mauguin symbol",
"x-optimade-type": "string",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "hm_symbol",
"label": "hm_symbol_pointgroups"
},
"type": [
"string",
"null"
],
"description": "Hermann-Mauguin point-group symbol used as the key and display symbol for a point-group record.\n\nThe value is one of the 32 crystallographic point-group symbols in Hermann-Mauguin notation, written in ASCII with `-` denoting rotoinversion.",
"x-optimade-unit": "inapplicable",
"enum": [
"1",
"-1",
"2",
"m",
"2/m",
"222",
"mm2",
"mmm",
"4",
"-4",
"4/m",
"422",
"4mm",
"-42m",
"4/mmm",
"3",
"-3",
"32",
"3m",
"-3m",
"6",
"-6",
"6/m",
"622",
"6mm",
"-62m",
"6/mmm",
"23",
"m-3",
"432",
"-43m",
"m-3m",
null
],
"examples": [
"1",
"-1",
"m-3m"
]
},
"is_centrosymmetric": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/is_centrosymmetric",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "is centrosymmetric",
"$comment": "Generated from data-generators JSON-LD fields without external definition URLs.",
"x-optimade-type": "boolean",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "is_centrosymmetric",
"label": "is_centrosymmetric_pointgroups"
},
"type": [
"boolean",
"null"
],
"description": "Boolean flag indicating whether the point group contains inversion symmetry.",
"x-optimade-unit": "inapplicable",
"examples": [
false,
true
]
},
"laue_class": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/laue_class",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Laue class",
"x-optimade-type": "string",
"x-compatibility": [
"https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group.Laue_class.html"
],
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "laue_class",
"label": "laue_class_pointgroups"
},
"type": [
"string",
"null"
],
"description": "The Laue class associated with the space group or point group.\n\nThe Laue class groups point groups that become equivalent when inversion symmetry is included.\n\nIt is the centrosymmetric point-group type generated by the original point group together with inversion.\nIts use as diffraction symmetry invokes the usual Friedel-pair equivalence; anomalous-scattering measurements need not have that intensity symmetry.",
"x-optimade-unit": "inapplicable",
"enum": [
"-1",
"2/m",
"mmm",
"4/m",
"4/mmm",
"-3",
"-3m",
"6/m",
"6/mmm",
"m-3",
"m-3m",
null
],
"examples": [
"-1",
"2/m"
]
},
"n_conjugacy_classes": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/n_conjugacy_classes",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Number of conjugacy classes",
"x-optimade-type": "integer",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "n_conjugacy_classes",
"label": "n_conjugacy_classes_pointgroups"
},
"type": [
"integer",
"null"
],
"description": "Number of conjugacy classes in the crystallographic point group.\n\nThis value MUST equal the length of the `conjugacy_classes` list of the point-group entry.\n\nIt also equals the number of complex irreducible rows in `character_table_complex`, but need not equal the number of rows in `character_table_real`.",
"x-optimade-unit": "inapplicable",
"examples": [
1,
2
]
},
"order": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/order",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Order of the point group",
"x-optimade-type": "integer",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "order",
"label": "order_pointgroups"
},
"type": [
"integer",
"null"
],
"description": "Order of the point group, i.e. the number of operations in the finite point group.\n\nThis value MUST equal the length of the `symops` list of the point-group entry.",
"x-optimade-unit": "inapplicable",
"examples": [
1,
2
]
},
"schoenflies": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/schoenflies",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Schoenflies symbol",
"x-optimade-type": "string",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "schoenflies",
"label": "schoenflies_pointgroups"
},
"type": [
"string",
"null"
],
"description": "The Schoenflies symbol for the crystallographic point group.\n\nThe value is one of the 32 crystallographic point-group symbols in Schoenflies notation, written in ASCII without subscript formatting.\nThe symbol `S6` is used for the point group also known as `C3i`.",
"x-optimade-unit": "inapplicable",
"enum": [
"C1",
"Ci",
"C2",
"Cs",
"C2h",
"D2",
"C2v",
"D2h",
"C4",
"S4",
"C4h",
"D4",
"C4v",
"D2d",
"D4h",
"C3",
"S6",
"D3",
"C3v",
"D3d",
"C6",
"C3h",
"C6h",
"D6",
"C6v",
"D3h",
"D6h",
"T",
"Th",
"O",
"Td",
"Oh",
null
],
"examples": [
"C1",
"C2v",
"Oh"
]
},
"symops": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/symops",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Symmetry operations",
"x-optimade-type": "list",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "symops",
"label": "symops_pointgroups"
},
"x-optimade-unit": "inapplicable",
"type": [
"array",
"null"
],
"description": "Full list of symmetry-operation descriptors for a point group.\nEach list member is an `op` object as defined by `/defs/v0.1/properties/symmetry/op`.\nPoint-group operations have a zero translation part, so the `screw_glide` and `origin_shift` classification fields are omitted.\n\n**Requirements/Conventions**:\n\n- It MUST be a list of dictionaries.\n- Each dictionary MUST follow the schema inherited from `/defs/v0.1/properties/symmetry/op`.\n\nThe matrices act on fractional column coordinates in the generator's reference lattice frame, not directly on Cartesian vectors.\nIn particular the hexagonal-axis matrices need not satisfy `W^T*W = I` although they are physical isometries of the appropriate metric.\nCharacter traces are independent of this basis choice; Cartesian polynomial bases are documented separately in `character_table_real`.\nThe order of this list is authoritative for operation indices in `conjugacy_classes`.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/symmetry/op",
"title": "Operation",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "op",
"label": "op_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "Information related to a crystallographic operation acting within one coordinate setting.\n\nRepresents an affine_transformation that is a crystallographic operation within one setting.\nThe affine map itself is stored in the embedded `affine_transformation` field.\nThe remaining fields classify the operation crystallographically, for example by rotation type, axis, sense, and screw or glide component.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **affine\\_transformation**: REQUIRED; Dictionary.\n Exact affine map for the operation.\n It MUST follow `/defs/v0.1/properties/symmetry/affine_transformation`.\n\n - **operation\\_kind**: OPTIONAL; String.\n The value `euclidean` identifies an operation emitted within a Euclidean-normalizer table; ordinary point-group and space-group operation records omit it.\n\n - **rot\\_type**: OPTIONAL; String.\n Crystallographic operation-type label for the linear part.\n\n - **axis**: OPTIONAL; List of 3 Integers.\n Operation axis or invariant direction using the integer-vector convention returned by the generator.\n\n - **sense**: OPTIONAL; Integer.\n Rotation sense/sign convention returned by the generator; `0` is used when no handed rotation sense is applicable.\n\n - **screw\\_glide**: OPTIONAL; List of 3 Fractions (String).\n Screw-axis or glide-plane component associated with a space-group affine operation.\n\n - **origin\\_shift**: OPTIONAL; List of 3 Fractions (String).\n Origin shift associated with the screw/glide decomposition of a space-group affine operation.\n\n- Whether the operation is proper follows from the sign of the `det` field of `affine_transformation`; no separate properness flag is stored.\n\nWriting the affine part as `(W,w)`, the intrinsic translation `screw_glide = v` is defined by `(W,w)^n = (I,n*v)`, where `n` is the order of `W`.\nThe reported `origin_shift = q` satisfies `(I-W)*q = w-v`; moving the coordinate origin to `q` leaves the intrinsic translation `v`.\nIt locates the symmetry element and is not a second translation to add to `w`.\nFor a proper rotation, `axis` is the integer direction fixed by `W`; for a rotoinversion it is the rotation axis fixed by `-W`, hence for a mirror it is the plane-normal direction.\nThese are direct-lattice direction components, not Cartesian unit vectors or reciprocal-plane indices.\nThe identity and inversion use `[0,0,0]` because neither has a unique axis.\nThe signed `sense` follows cctbx's rotation/rotoinversion convention about that reported axis; converting a rotoinversion to a Schoenflies rotation-reflection symbol can reverse the rotation sense.",
"properties": {
"affine_transformation": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/symmetry/affine_transformation",
"title": "Affine transformation",
"x-optimade-type": "dictionary",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "affine_transformation",
"label": "affine_transformation_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"description": "An affine transformation acting on fractional crystallographic coordinates.\n\nAn invertible affine transformation preserves collinearity and parallelism, but need not preserve Euclidean distances or angles.\nA singular affine map can collapse a line or plane to a lower-dimensional image.\nThe transformation is represented by a 3 by 3 matrix and a 3-vector, both serialized with exact string entries.\nWith column vectors, the map is `u_out = matrix * u_in + vector`; matrix rows specify the three output components.\nThe containing property identifies whether `u_in` denotes fractional coordinates or abstract Wyckoff parameters and identifies the input and output settings.\nNo wrapping modulo lattice translations is implicit in this equation; apply any required periodic reduction only in the specified output setting.\nThe transformation may, for example, represent an operation within one setting, a setting transform, a subgroup embedding, a normalizer representative, or a parametric coordinate map for a Wyckoff-position orbit representative.\nWhen used as a parametric coordinate map, the matrix may be singular because special Wyckoff positions can constrain or identify parameters.\n\n**Requirements/Conventions**:\n\n- It MUST be a dictionary with the following keys:\n\n - **matrix**: REQUIRED; Exact 3x3 matrix.\n Matrix part of the affine transformation.\n It MUST be represented as a list of three row lists, each containing three exact rational entries represented as strings.\n\n - **vector**: REQUIRED; List of 3 Fractions (String).\n Translation or origin-shift vector of the affine transformation in fractional coordinates.\n\n - **xyz**: OPTIONAL; String.\n Coordinate expression for the affine transformation in `x,y,z` notation when available.\n It MUST express the same affine map as `matrix` and `vector`, using `x,y,z` for the input components.\n\n - **det**: OPTIONAL; Integer.\n Determinant of `matrix` when the generator emits it.\n\n - **is\\_orthogonal**: OPTIONAL; Boolean.\n Whether the linear part preserves the crystallographic metric family specified by the containing setting; this is not a test of the fractional matrix against the Cartesian identity metric.",
"properties": {
"matrix": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice",
"dim_lattice"
],
"sizes": [
3,
3
]
},
"type": [
"array",
"null"
],
"description": "Exact 3 by 3 matrix part of the affine transformation.",
"items": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array"
],
"description": "One row of the exact 3 by 3 matrix.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
}
},
"vector": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Exact fractional-coordinate vector part of the affine transformation.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
},
"xyz": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/symmetry/op_xyz",
"title": "Operation xyz",
"x-optimade-type": "string",
"x-compatibility": [
"https://schemas.optimade.org/defs/v1.2/properties/optimade/common/symmetry_operation_xyz",
"https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html"
],
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "op_xyz",
"label": "op_xyz_symmetry"
},
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Coordinate operation expressed in the algebraic xyz form, also known as Jones' faithful representation (Bradley & Cracknell, 1972: pp. 35-37; adapted for computer strings).\n\nThe following definition is adapted from (and meant to be compatible with) the IUCr symCIF version 1.0.1 dictionary definition of `_space_group_symop.operation_xyz` referenced to: International Tables for Crystallography (2002). Volume A, Space-group symmetry, edited by Th. Hahn, 5th. ed. (Kluwer Academic Publishers).\nIt is available at: https://www.iucr.org/__data/iucr/cifdic_html/2/cif_sym.dic/Ispace_group_symop.operation_xyz.html\n\nIf W is a matrix representation of the rotational part of the symmetry operation defined by the positions and signs of x, y and z, and w is a column of translations defined by the fractions, an equivalent position X' is generated from a given position X by the equation: X' = WX + w.",
"x-undef-pattern": "^([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?),([-+]?[xyz]([-+][xyz])?([-+](1/2|[12]/3|[1-3]/4|[1-5]/6))?|[-+]?(1/2|[12]/3|[1-3]/4|[1-5]/6)([-+][xyz]([-+][xyz])?)?)$",
"examples": [
"-x,-y,z",
"x,1/2-y,1/2+z"
]
},
"det": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"type": [
"integer",
"null"
],
"description": "Determinant of the matrix part when emitted by the generator.\nThis optional integer annotation MUST equal the exact determinant of `matrix`; its absence does not imply determinant one.\nRational matrices can have noninteger determinants, in which case this integer annotation is omitted."
},
"is_orthogonal": {
"x-optimade-type": "boolean",
"x-optimade-unit": "inapplicable",
"type": [
"boolean",
"null"
],
"description": "Whether the matrix part is an isometry of the setting's metric, i.e. it preserves every metric tensor of the setting's crystal family expressed in this basis.\nFor a same-setting matrix `M` and metric tensor `g`, the criterion is `M^T g M = g` for every positive-definite metric in that family.\nThis is orthogonality with respect to the actual (generally non-Cartesian) lattice metric, not orthogonality of the matrix as a plain array: hexagonal sixfold rotations are isometries, whereas a cell-enlarging transform is not."
}
},
"examples": [
{
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"-1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,-y,z",
"det": 1,
"is_orthogonal": true
}
]
},
"operation_kind": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string"
],
"enum": [
"euclidean"
],
"description": "Euclidean-normalizer context when present; this does not change the operation's affine action."
},
"rot_type": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Symbolic crystallographic operation-type label for the linear part.",
"enum": [
"1",
"-1",
"2",
"m",
"3",
"-3",
"4",
"-4",
"6",
"-6",
null
]
},
"axis": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Integer-vector axis or invariant-direction descriptor for the operation.",
"items": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"type": [
"integer"
],
"description": "One integer component of the axis vector."
}
},
"sense": {
"x-optimade-type": "integer",
"x-optimade-unit": "inapplicable",
"type": [
"integer",
"null"
],
"description": "Rotation sense/sign convention returned by the generator; zero for identity, inversion, twofold rotation, and mirror operations.",
"enum": [
-1,
0,
1,
null
]
},
"screw_glide": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Screw-axis or glide-plane component represented exactly as a list of fraction strings.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
},
"origin_shift": {
"x-optimade-type": "list",
"x-optimade-unit": "inapplicable",
"x-optimade-dimensions": {
"names": [
"dim_lattice"
],
"sizes": [
3
]
},
"type": [
"array",
"null"
],
"description": "Origin-shift descriptor represented exactly as a list of fraction strings.",
"items": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/core/fraction",
"title": "Fraction",
"x-optimade-type": "string",
"x-optimade-definition": {
"label": "fraction_core",
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "fraction"
},
"type": [
"string",
"null"
],
"description": "A numerical representation formed as the quotient of two numbers represented as a string.",
"examples": [
"2/3",
"5/42",
"10",
"0"
],
"x-optimade-unit": "inapplicable"
}
}
},
"examples": [
{
"affine_transformation": {
"matrix": [
[
"-1",
"0",
"0"
],
[
"0",
"-1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "-x,-y,z",
"det": 1,
"is_orthogonal": true
},
"rot_type": "2",
"sense": 0,
"axis": [
0,
0,
1
],
"screw_glide": [
"0",
"0",
"0"
],
"origin_shift": [
"0",
"0",
"0"
]
}
]
},
"examples": [
[
{
"affine_transformation": {
"matrix": [
[
"1",
"0",
"0"
],
[
"0",
"1",
"0"
],
[
"0",
"0",
"1"
]
],
"vector": [
"0",
"0",
"0"
],
"xyz": "x,y,z",
"det": 1,
"is_orthogonal": true
},
"rot_type": "1",
"sense": 0,
"axis": [
0,
0,
0
]
}
]
]
},
"schoenflies_markup": {
"$id": "https://schemas.httk.org/defs/v0.1/properties/pointgroups/schoenflies_markup",
"x-optimade-requirements": {
"support": "may",
"sortable": false,
"query-support": "none",
"response-level": "may"
},
"title": "Schoenflies symbol markups",
"x-optimade-definition": {
"kind": "property",
"version": "0.1.0",
"format": "1.3",
"name": "schoenflies_markup",
"label": "schoenflies_markup_pointgroups"
},
"description": "Display-oriented renderings of the Schoenflies symbol in `schoenflies`.\nThe plain string value is stored in the corresponding unsuffixed property; this object only provides alternate markup forms for display.",
"x-optimade-type": "dictionary",
"x-optimade-unit": "inapplicable",
"type": [
"object",
"null"
],
"properties": {
"html": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "HTML rendering of the sibling string."
},
"latex": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "LaTeX rendering of the sibling string."
},
"unicode": {
"x-optimade-type": "string",
"x-optimade-unit": "inapplicable",
"type": [
"string",
"null"
],
"description": "Unicode rendering of the sibling string."
}
},
"examples": [
{
"html": "<i>P</i> 2<sub>1</sub>/<i>c</i>",
"latex": "\\mathit{P}\\,2_{1}/c",
"unicode": "P2\u2081/c"
}
]
}
}
},
"examples": [
[
{
"hm_symbol": "2/m",
"order": 4
}
]
]
}