# Crystal pattern

### From Online Dictionary of Crystallography

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<font color="blue">Motif cristallin</font> (''Fr''). <font color="red">Unendlicher Idealkristall</font> (''Ge''). <font color="black">Motivo cristallino</font>(''It''). <font color="purple">結晶模様</font> (''Ja''). <font color="green">Cristal ideal infinito</font> (''Sp''). | <font color="blue">Motif cristallin</font> (''Fr''). <font color="red">Unendlicher Idealkristall</font> (''Ge''). <font color="black">Motivo cristallino</font>(''It''). <font color="purple">結晶模様</font> (''Ja''). <font color="green">Cristal ideal infinito</font> (''Sp''). | ||

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+ | '''Synonym''': ''infinite ideal crystal'' | ||

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An object in the ''n''-dimensional [[point space]] ''E<sup>n</sup>'' is called an ''n''-dimensional '''crystallographic pattern''' or, for short, '''crystal pattern''' if among its symmetry operations: | An object in the ''n''-dimensional [[point space]] ''E<sup>n</sup>'' is called an ''n''-dimensional '''crystallographic pattern''' or, for short, '''crystal pattern''' if among its symmetry operations: |

## Latest revision as of 15:33, 16 November 2018

Motif cristallin (*Fr*). Unendlicher Idealkristall (*Ge*). Motivo cristallino(*It*). 結晶模様 (*Ja*). Cristal ideal infinito (*Sp*).

**Synonym**: *infinite ideal crystal*

An object in the *n*-dimensional point space *E ^{n}* is called an

*n*-dimensional

**crystallographic pattern**or, for short,

**crystal pattern**if among its symmetry operations:

- there are
*n*translations, the translation vectors**t**_{1}, ... ,**t**_{n}of which are linearly independent; - all translation vectors, except the zero vector
**0**, have a length of at least*d*> 0.

When the crystal pattern consists of atoms, it takes the name of **crystal structure**. The crystal pattern is thus the generalization of a crystal structure to any pattern, concrete or abstract, in any dimension, which obeys the conditions of periodicity and discreteness expressed above.

## See also

- Point space
- Noncrystallographic symmetry
*International Tables for Crystallography, Volumes A*and*A1*