# Bravais arithmetic class

(Difference between revisions)
 Revision as of 15:39, 30 May 2019 (view source)m (moved Bravais class to Bravais arithmetic class: Modified to comply with the new terminology in the 6th edition of ITA.)← Older edit Revision as of 15:39, 30 May 2019 (view source) (Modified to comply with the new terminology in the 6th edition of ITA.)Newer edit → Line 2: Line 2: == Definition == == Definition == - An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class'', or '''Bravais class''' for short. + 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 class, and each matrix group of a Bravais class represents the point group of a lattice referred to an appropriate primitive basis.

## Revision as of 15:39, 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 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:

• 2p
• 2mmp
• 2mmc
• 4mmp
• 6mmh

There exist 14 Bravais 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