# Bravais arithmetic class

### From Online Dictionary of Crystallography

##### Revision as of 15:50, 30 May 2019 by MassimoNespolo (talk | contribs) (modified to comply with the revised nomenclature in the 6th edition of ITA)

Revision as of 15:50, 30 May 2019 by MassimoNespolo (talk | contribs) (modified to comply with the revised nomenclature in the 6th edition of ITA)

Classe arithmétique de Bravais (*Fr*). Bravais Arithmetische Klasse (*Ge*). Classe aritmetica di Bravais (*It*). ブラベー代数的類 (*Ja*). Clase aritmética 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