In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron.
Rhombic Dodecahedral Honeycomb
The rhombic dodecahedral honeycomb (also dodecahedrille) is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It is the Voronoi diagram of the face-centered cubic sphere-packing, which has the densest possible packing of equal spheres in ordinary space (see Kepler conjecture).
In Dungeons and Dragons
“I’ve never seen a rhombic dodecahedron d12 before. They do exist after a quick search, but the much more common d12 is just a dodecahedron, with pentagonal faces.”
The UCLA1 investigators developed a technique that prevents that corrosion and showed that, in its absence, lithium atoms assemble into a surprising shape—the rhombic dodecahedron, a 12-sided figure similar to the dice used in role-playing games like Dungeons and Dragons.
University of California, Los Angeles ↩