# Difference between revisions of "Bravais arithmetic class"

### From Online Dictionary of Crystallography

(Modified to comply with the new terminology in the 6th edition of ITA.) |
(Modified to comply with the new terminology in the 6th edition of ITA.) |
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An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class''. | An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class''. | ||

− | Each lattice is associated with a Bravais class, and each matrix group of a Bravais class represents the point group of a lattice referred to an appropriate primitive basis. | + | Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis. |

− | There exist 5 Bravais classes in two dimensions: | + | There exist 5 Bravais arithmetic classes in two dimensions: |

* 2''p'' | * 2''p'' | ||

* 2''mmp'' | * 2''mmp'' | ||

Line 13: | Line 13: | ||

* 6''mmh'' | * 6''mmh'' | ||

− | There exist 14 Bravais classes in three dimensions: | + | There exist 14 Bravais arithmetic classes in three dimensions: |

* <math>{\bar 1}</math>''P'' | * <math>{\bar 1}</math>''P'' | ||

* 2/''mP'' | * 2/''mP'' | ||

Line 30: | Line 30: | ||

== See also == | == See also == | ||

− | *[[Bravais | + | *[[Bravais class]] |

*Chapter 1.3.4.3 of ''International Tables for Crystallography, Volume A'', 6th edition | *Chapter 1.3.4.3 of ''International Tables for Crystallography, Volume A'', 6th edition | ||

[[category: Fundamental crystallography]] | [[category: Fundamental crystallography]] |

## Revision as of 15:40, 30 May 2019

Classe de Bravais (*Fr*). Bravais-Klasse (*Ge*). Classe di Bravais (*It*). ブラベー類 (*Ja*). Clase de Bravais (*Sp*).

## Definition

An arithmetic crystal class with matrix group of lattices is called a *Bravais arithmetic crystal class*.

Each lattice is associated with a Bravais arithmetic class, and each matrix group of a Bravais arithmetic class represents the point group of a lattice referred to an appropriate primitive basis.

There exist 5 Bravais arithmetic classes in two dimensions:

- 2
*p* - 2
*mmp* - 2
*mmc* - 4
*mmp* - 6
*mmh*

There exist 14 Bravais arithmetic classes in three dimensions:

- [math]{\bar 1}[/math]
*P* - 2/
*mP* - 2/
*mS* -
*mmmP* -
*mmmS* -
*mmmI* -
*mmmF* - 4/
*mmmP* - 4/
*mmmI* - [math]{\bar 3}[/math]
*mR* - 6/
*mmmP* -
*m*[math]{\bar 3}[/math]*mP* -
*m*[math]{\bar 3}[/math]*mI* -
*m*[math]{\bar 3}[/math]*mF*

## See also

- Bravais class
- Chapter 1.3.4.3 of
*International Tables for Crystallography, Volume A*, 6th edition