Difference between revisions of "Bravais arithmetic class"

From Online Dictionary of Crystallography

(Modified to comply with the new terminology in the 6th edition of ITA.)
(modified to comply with the revised nomenclature in the 6th edition of ITA)
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<font color="blue">Classe de Bravais</font> (''Fr''). <font color="red">Bravais-Klasse</font> (''Ge''). <font color="black">Classe di Bravais</font> (''It''). <font color="purple">ブラベー類</font> (''Ja''). <font color="green">Clase de Bravais</font> (''Sp'').
<font color="blue">Classe arithmétique de Bravais</font> (''Fr''). <font color="red">Bravais Arithmetische Klasse</font> (''Ge''). <font color="black">Classe aritmetica di Bravais</font> (''It''). <font color="purple">ブラベー代数的類</font> (''Ja''). <font color="green">Clase aritmética de Bravais</font> (''Sp'').
== Definition ==
== Definition ==

Latest revision as of 15:50, 30 May 2019

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