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 diamond crystal structure belongs to the face-centered cubic lattice, with a repeated two-atom pattern.
Hexagonal hanksite crystal, with threefold c-axis symmetry

Their corresponding space groups are assigned to a lattice system.

- Crystal system

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.

- Space group
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.

3 related topics

Alpha

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.

A rock containing three crystals of pyrite (FeS2). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets.

Cubic crystal system

A rock containing three crystals of pyrite (FeS2). The crystal structure of pyrite is primitive cubic, and this is reflected in the cubic symmetry of its natural crystal facets.
A network model of a primitive cubic system
The primitive and cubic close-packed (also known as face-centered cubic) unit cells
Visualisation of a diamond cubic unit cell: 1. Components of a unit cell, 2. One unit cell, 3. A lattice of 3 x 3 x 3 unit cells
A caesium chloride unit cell. The two colors of spheres represent the two types of atoms.
This graphic shows the interlocking simple cubic lattices of cesium and chlorine. You can see them separately and as they are interlocked in what looks like a body-centered cubic arrangement
The rock-salt crystal structure. Each atom has six nearest neighbours, with octahedral geometry.
A zincblende unit cell
The structure of the Heusler compounds with formula X2YZ (e. g., Co2MnSi).
Diagram of the iron monosilicide structure.
Weaire–Phelan structure

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.

Relation between the two settings for the rhombohedral lattice

Hexagonal crystal family

Relation between the two settings for the rhombohedral lattice
Hexagonal close packed (hcp) unit cell
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).

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).