# Difference between revisions of "Bravais arithmetic class"

### From Online Dictionary of Crystallography

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

*[[Bravais flock]] | *[[Bravais flock]] | ||

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

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

## Revision as of 09:33, 13 May 2017

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

## Definition

An arithmetic crystal class with matrix group of lattices is called a *Bravais arithmetic crystal class*, or **Bravais class** for short.

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.

There exist 5 Bravais classes in two dimensions:

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

There exist 14 Bravais 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 flock
- Chapter 1.3.4.3 of
*International Tables for Crystallography, Volume A*, 6th edition