Eigensymmetry

From Online Dictionary of Crystallography

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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'').  
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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'').
== Definition ==
== Definition ==

Revision as of 17:35, 8 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