Eigensymmetry

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