Bravais arithmetic class

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(Modified to comply with the new terminology in the 6th edition of ITA.)
(Modified to comply with the new terminology in the 6th edition of ITA.)
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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''.
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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:
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There exist 5 Bravais arithmetic classes in two dimensions:
* 2''p''
* 2''p''
* 2''mmp''
* 2''mmp''
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* 6''mmh''
* 6''mmh''
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There exist 14 Bravais classes in three dimensions:
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There exist 14 Bravais arithmetic classes in three dimensions:
* <math>{\bar 1}</math>''P''
* <math>{\bar 1}</math>''P''
* 2/''mP''
* 2/''mP''
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== See also ==
== See also ==
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*[[Bravais flock]]
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*[[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