Composite lattices For composite lattices, (crystals which have more than one vector in their basis) each single lattice point represents multiple atoms. We can break apart each Wigner–Seitz cell into subcells by further Voronoi decomposition according to the closest atom, instead of the closest lattice point. For example, the diamond crystal structure contains a two atom basis. In diamond, carbon atoms have tetrahedral sp3 bonding, but since tetrahedra do not tile space, the voronoi decomposition of the diamond crystal structure is actually the triakis truncated tetrahedral honeycomb. Another example is applying Voronoi decomposition to the atoms in the A15 phases, which forms the polyhedral approximation of the Weaire–Phelan structure. Symmetry The Wigner–Seitz cell always has the same point symmetry as the underlying Bravais lattice. For example, the cube, truncated octahedron, and rhombic dodecahedron have point symmetry Oh, since the respective Bravais lattices used to generate them all belong to the cubic lattice system, which has Oh point symmetry. Brillouin zone In practice, the Wigner–Seitz cell itself is actually rarely used as a description of direct space, where the conventional unit cells are usually used instead. However, the same decomposition is extremely important when applied to reciprocal space. The Wigner–Seitz cell in the reciprocal space is called the Brillouin zone, which contains the information about whether a material will be a conductor, semiconductor or an insulator. See also Delaunay triangulation Coordination geometry Crystal field theory Wigner crystal References Crystallography Mineralogy