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Difference between revisions of "Eigensymmetry"

From Online Dictionary of Crystallography

(Tidied translations and corrected Spanish (U. Mueller))
 
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<Font color="blue"> Symétrie propre </Font> (''Fr).
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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 ==
  
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. For instance, 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.
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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 crystalline form, considered as a polyhedron by itself. The eigensymmetry point group is either the generating point group itself or a supergroup of it.
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== Examples ==
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*The [[space group]] of a [[crystal pattern|crystal structure]] is the intersection of the eigensymmetries of the [[crystallographic orbit]]s building the structure.
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*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.
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*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 ==
 
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*Chapters 3.2.1.2.2 and 3.4.1.3 of ''International Tables for Crystallography, Volume A'', 6th edition
Chapter 10.1 of ''International Tables of Crystallography, Volume A''<br>
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*Chapter 3.3 of ''International Tables for Crystallography, Volume D''
Chapter 3.3 of ''International Tables of Crystallography, Volume D''<br>
 
  
 
[[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