On 19 Dec 2003, sujeet kumar wrote:

> What is the voronoi polyhedron for the hexagonal(3D) lattice?

A hexagonal prism. John Conway

In general, there are only five possible topological shapes

the Voronoi cell of a 3-dimensional lattice can be, exemplified

by the truncated octahedron, the hexarhombic dodecahedron, the

rhombic dodecahedron, the hexagonal prism, and the cube. You

can find a proof in my book "The Sensual Form"

The Voronoi cell of the configuartion of carbon atoms in a diamond

(which is NOT a lattice) is a triakis truncated tetrahedron.

John Conway