# Bravais arithmetic class

(Difference between revisions)
 Revision as of 15:40, 30 May 2019 (view source) (Modified to comply with the new terminology in the 6th edition of ITA.)← Older edit Latest revision as of 15:50, 30 May 2019 (view source) (modified to comply with the revised nomenclature in the 6th edition of ITA) Line 1: Line 1: - Classe de Bravais (''Fr''). Bravais-Klasse (''Ge''). Classe di Bravais (''It''). ブラベー類 (''Ja''). Clase de Bravais (''Sp''). + 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 == == Definition ==

## Latest revision as of 15:50, 30 May 2019

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:

• 2p
• 2mmp
• 2mmc
• 4mmp
• 6mmh

There exist 14 Bravais arithmetic classes in three dimensions:

• ${\bar 1}$P
• 2/mP
• 2/mS
• mmmP
• mmmS
• mmmI
• mmmF
• 4/mmmP
• 4/mmmI
• ${\bar 3}$mR
• 6/mmmP
• m${\bar 3}$mP
• m${\bar 3}$mI
• m${\bar 3}$mF