Bravais arithmetic class

From Online Dictionary of Crystallography

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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).


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:

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