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httk property definitionsProperty definitions using the OPTIMADE property definition format, hosted by httk
Note: prerelease version v0.1, subject to change

Maximal subgroup type (property)

This page documents an OPTIMADE Property Definition. See https://schemas.optimade.org/ for more information.

ID: https://schemas.httk.org/defs/v0.1/properties/transformations/subgroup_type
Definition name: subgroup_type

Property name: Maximal subgroup type
Description: International Tables maximal subgroup class.
Type: string

The value is t for a translationengleiche subgroup and k for a klassengleiche subgroup. The field is omitted for identity embeddings, for general subgroups that lose both translations and point symmetry, and for records that are not subgroup embeddings. Its presence does not by itself certify maximality; the relation table containing the record supplies that information.

A translationengleiche subgroup retains the complete translation lattice and loses point symmetry: i_T = 1, i_P > 1. A klassengleiche subgroup retains the point group and loses translations: i_P = 1, i_T > 1. For a maximal proper subgroup these are the alternatives; a subgroup losing both is not represented by either value. The underlying t/k classification describes what symmetry is lost and does not by itself prove that an embedding is maximal.

Examples:

Formats: [JSON] [MD]

JSON definition:

{
    "$id": "https://schemas.httk.org/defs/v0.1/properties/transformations/subgroup_type",
    "$schema": "https://schemas.optimade.org/meta/v1.3/optimade/property_definition.json",
    "title": "Maximal subgroup type",
    "x-optimade-type": "string",
    "x-optimade-definition": {
        "kind": "property",
        "version": "0.1.0",
        "format": "1.3",
        "name": "subgroup_type",
        "label": "subgroup_type_transformations"
    },
    "type": [
        "string"
    ],
    "description": "International Tables maximal subgroup class.\n\nThe value is `t` for a translationengleiche subgroup and `k` for a klassengleiche subgroup.\nThe field is omitted for identity embeddings, for general subgroups that lose both translations and point symmetry, and for records that are not subgroup embeddings.\nIts presence does not by itself certify maximality; the relation table containing the record supplies that information.\n\nA translationengleiche subgroup retains the complete translation lattice and loses point symmetry: `i_T = 1`, `i_P > 1`.\nA klassengleiche subgroup retains the point group and loses translations: `i_P = 1`, `i_T > 1`.\nFor a maximal proper subgroup these are the alternatives; a subgroup losing both is not represented by either value.\nThe underlying t/k classification describes what symmetry is lost and does not by itself prove that an embedding is maximal.",
    "enum": [
        "t",
        "k"
    ],
    "x-optimade-unit": "inapplicable",
    "examples": [
        "k",
        "t"
    ]
}