# Lattice system

### From Online Dictionary of Crystallography

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

## Contents |

## 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