# Bravais arithmetic class

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 Revision as of 15:39, 30 May 2019 (view source) (Modified to comply with the new terminology in the 6th edition of ITA.)← Older edit Revision as of 15:40, 30 May 2019 (view source) (Modified to comply with the new terminology in the 6th edition of ITA.)Newer edit → Line 4: Line 4: 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: * ${\bar 1}$''P'' * ${\bar 1}$''P'' * 2/''mP'' * 2/''mP'' Line 30: Line 30: == See also == == See also == - *[[Bravais flock]] + *[[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:

• 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

## See also

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