Bravais arithmetic class

Classe de Bravais (Fr). Bravais Klasse (Ge). Classe di Bravais (It). ブラベー類(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

• Bravais flock
• Chapter 1.3.4.3 in of International Tables for Crystallography, Volume A, 6th edition