Their corresponding space groups are assigned to a lattice system.

- Crystal systemThe space groups in three dimensions are made from combinations of the 32 crystallographic point groups with the 14 Bravais lattices, each of the latter belonging to one of 7 lattice systems.

- Space group3 related topics

## Bravais lattice

Infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by:

Infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by:

The 14 possible symmetry groups of Bravais lattices are 14 of the 230 space groups.

In two-dimensional space there are 5 Bravais lattices, grouped into four crystal families, shown in the table below.

## Cubic crystal system

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube.

The isometric crystal system class names, point groups (in Schönflies notation, Hermann–Mauguin notation, orbifold, and Coxeter notation), type, examples, International Tables for Crystallography space group number, and space groups are listed in the table below.

## Hexagonal crystal family

In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral).

A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system (see table in Crystal system).