> 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.