Lattice system

Système réticulaire (Fr); Sistema reticolare (It); 格子系 (Ja)

Definition

A lattice system of space groups contains complete Bravais flocks. All those Bravais flocks which intersect exactly the same set of geometric crystal classes belong to the same lattice system.

Alternative definition

A lattice system of space groups contains complete Bravais flocks. All those Bravais flocks belong to the same lattice system for which the Bravais classes belong to the same (holohedral) geometric crystal class.

Lattice systems in two and three dimensions

In the two-dimensional space there exist four lattice systems:

• monoclinic
• orthorhombic
• tetragonal
• hexagonal

In the three-dimensional space there exist seven lattice systems:

• triclinic
• monoclinic
• orthorhombic
• tetragonal
• rhombohedral
• hexagonal
• cubic

Note that the adjective trigonal refers to a crystal system, not to a lattice system. Rhombohedral crystals belong to the trigonal crystal system, but trigonal crystals may belong to the rhombohedral or to the hexagonal lattice system.

Note

In previous editions of Volume A of the International Tables of Crystallography (before 2002), the lattice systems were called Bravais systems.

See also

• Section 1.3.4.4.2 in of International Tables of Crystallography, Volume A, 6^th edition