# Lattice system

### From Online Dictionary of Crystallography

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== Definition == | == Definition == | ||

- | A '''lattice system''' of space groups contains complete [[Bravais | + | A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes which intersect exactly the same set of [[geometric crystal class]]es belong to the same lattice system. |

== Alternative definition == | == Alternative definition == | ||

- | A '''lattice system''' of space groups contains complete [[Bravais | + | A '''lattice system''' of space groups contains complete [[Bravais class]]es. All those Bravais classes belong to the same lattice system for which the [[Bravais arithmetic class]]es belong to the same (holohedral) [[geometric crystal class]]. |

== Lattice systems in two and three dimensions == | == Lattice systems in two and three dimensions == |

## Latest revision as of 17:23, 30 May 2019

Système réticulaire (*Fr*). Gittersystem (*Ge*). Sistema reticolare (*It*). 格子系 (*Ja*).

## Contents |

## Definition

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

## Lattice systems in two and three dimensions

In two-dimensional space there exist four lattice systems:

- monoclinic
- orthorhombic
- tetragonal
- hexagonal

In 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 *International Tables of Crystallography* (before 2002), the lattice systems were called *Bravais systems*.

## See also

- Bravais class
- Chapter 1.3.4.4.2 of
*International Tables for Crystallography, Volume A*, 6th edition