Relation between the two settings for the rhombohedral lattice
The diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.
Hexagonal close packed (hcp) unit cell
Hexagonal hanksite crystal, with threefold c-axis symmetry
Wurtzite unit cell as described by symmetry operators of the space group.
Another representation of the wurtzite unit cell
Another representation of the wurtzite structure
The unit cell of nickeline

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).

- Hexagonal crystal family

The various classifications are often confused: in particular the trigonal crystal system is often confused with the rhombohedral lattice system, and the term "crystal system" is sometimes used to mean one of the others.

- Crystal system
Relation between the two settings for the rhombohedral lattice

1 related topic

Alpha

The space group of hexagonal H2O ice is P63/mmc. The first m indicates the mirror plane perpendicular to the c-axis (a), the second m indicates the mirror planes parallel to the c-axis (b), and the c indicates the glide planes (b) and (c). The black boxes outline the unit cell.

Space group

Symmetry group of an object in space, usually in three dimensions.

Symmetry group of an object in space, usually in three dimensions.

The space group of hexagonal H2O ice is P63/mmc. The first m indicates the mirror plane perpendicular to the c-axis (a), the second m indicates the mirror planes parallel to the c-axis (b), and the c indicates the glide planes (b) and (c). The black boxes outline the unit cell.

The 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.

If the crystal system is trigonal, then the lattice system is hexagonal unless the space group is one of the seven in the rhombohedral lattice system consisting of the 7 trigonal space groups in the table above whose name begins with R. (The term rhombohedral system is also sometimes used as an alternative name for the whole trigonal system.) The hexagonal lattice system is larger than the hexagonal crystal system, and consists of the hexagonal crystal system together with the 18 groups of the trigonal crystal system other than the seven whose names begin with R.