Difference between revisions of "Bravais arithmetic class"
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An [[arithmetic crystal class]] with matrix group of lattices is called a ''Bravais arithmetic crystal class'', or '''Bravais class''' for short. | 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 | + | 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: | There exist 5 Bravais classes in two dimensions: | ||
Revision as of 08:41, 25 May 2007
Classe de Bravais (Fr). Bravais klass (Ge). Classe di Bravais (It). ブラベークラス(Ja)
Definition
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
Section 8.2.5 in of International Tables of Crystallography, Volume A