Difference between revisions of "Eigensymmetry"
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| + | <font color="blue">Symétrie propre</font> (''Fr''). <font color="red">Eigensymmetrie</font> (''Ge''). <font color="black">Simmetria propria</font> (''It''). <font color="purple">固有対称性</font> (''Ja''). <font color="green">Simetría propia</font> (''Sp''). | ||
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== Definition == | == Definition == | ||
| − | The ''eigensymmetry'', or ''inherent symmetry'', of a crystal is the point group or space group of a crystal, irrespective of its orientation and location in space | + | The ''eigensymmetry'', or ''inherent symmetry'', of a crystal is the point group or space group of a crystal, irrespective of its orientation and location in space. |
| − | In morphology, the eigensymmetry is the full symmetry of a | + | == Examples == |
| + | *The [[space group]] of a [[crystal pattern|crystal structure]] is the intersection of the eigensymmetries of the [[crystallographic orbit]]s building the structure. | ||
| + | *All individuals of a [[twin|twinned crystal]] have the same (or the enantiomorphic) eigensymmetry but may exhibit different orientations. The orientations of each of two twin components are related by a [[twin operation]] which cannot be part of the eigensymmetry. | ||
| + | *In morphology, the eigensymmetry is the full symmetry of a [[form|crystal form]], considered as a polyhedron by itself. The eigensymmetry point group is either the generating point group itself or a supergroup of it. | ||
== See also == | == See also == | ||
| − | + | *Chapters 3.2.1.2.2 and 3.4.1.3 of ''International Tables for Crystallography, Volume A'', 6th edition | |
| − | + | *Chapter 3.3 of ''International Tables for Crystallography, Volume D'' | |
| − | Chapter 3.3 of ''International Tables | ||
[[Category:Fundamental crystallography]] | [[Category:Fundamental crystallography]] | ||
Latest revision as of 09:40, 13 November 2017
Symétrie propre (Fr). Eigensymmetrie (Ge). Simmetria propria (It). 固有対称性 (Ja). Simetría propia (Sp).
Definition
The eigensymmetry, or inherent symmetry, of a crystal is the point group or space group of a crystal, irrespective of its orientation and location in space.
Examples
- The space group of a crystal structure is the intersection of the eigensymmetries of the crystallographic orbits building the structure.
- All individuals of a twinned crystal have the same (or the enantiomorphic) eigensymmetry but may exhibit different orientations. The orientations of each of two twin components are related by a twin operation which cannot be part of the eigensymmetry.
- In morphology, the eigensymmetry is the full symmetry of a crystal form, considered as a polyhedron by itself. The eigensymmetry point group is either the generating point group itself or a supergroup of it.
See also
- Chapters 3.2.1.2.2 and 3.4.1.3 of International Tables for Crystallography, Volume A, 6th edition
- Chapter 3.3 of International Tables for Crystallography, Volume D