Bravais arithmetic class

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). 布拉维算数类 (Zh).

Definition

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 crystal classes in two dimensions:

• [math] 2p [/math]
• [math] 2mmp [/math]
• [math] 2mmc [/math]
• [math] 4mmp [/math]
• [math] 6mmp [/math]

There exist 14 Bravais arithmetic crystal classes in three dimensions:

• [math] {\bar 1}P [/math]
• [math] 2/mP [/math]
• [math] 2/mC [/math]
• [math] mmmP [/math]
• [math] mmmC [/math]
• [math] mmmF [/math]
• [math] mmmI [/math]
• [math] 4/mmmP [/math]
• [math] 4/mmmI [/math]
• [math] {\bar 3}mR [/math]
• [math] 6/mmmP [/math]
• [math] m{\bar 3}mP [/math]
• [math] m{\bar 3}mF [/math]
• [math] m{\bar 3}mI [/math]

See also

• Bravais class
• Chapter 1.3.4.4 of International Tables for Crystallography, Volume A, 6th edition