Difference between revisions of "Bravais arithmetic class"

From Online Dictionary of Crystallography

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m (moved Bravais class to Bravais arithmetic class: Modified to comply with the new terminology in the 6th edition of ITA.)
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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).


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:

  • 2p
  • 2mmp
  • 2mmc
  • 4mmp
  • 6mmh

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 of International Tables for Crystallography, Volume A, 6th edition