Rhombic dodecahedral honeycomb cells. The vertices with the acute rhombic face angles have 6 cells. The rhombic dodecahedron can be twisted on one of its hexagonal cross-sections to form a trapezo-rhombic dodecahedron, which is the cell of a somewhat similar tessellation, the Voronoi diagram of hexagonal close-packing. The "rhombic dodecahedral honeycomb" can be dissected into a trigonal trapezohedral honeycomb with each rhombic dodecahedron dissected into 4 trigonal trapezohedrons. Each rhombic dodecahedra can also be dissected with a center point into 12 rhombic pyramids of the rhombic pyramidal honeycomb. The trapezo-rhombic dodecahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space. It consists
Icosahedral honeycomb part of a sequence of regular polychora and honeycombs {3,"p",3}: It a part of a sequence of regular polychora and honeycombs {"p",5,"p"}: There are nine uniform honeycombs in the [3,5,3] Coxeter group family, including this regular form as well as the bitruncated form, t{3,5,3}, , also called "truncated dodecahedral honeycomb", each of whose cells are truncated dodecahedra. The rectified icosahedral honeycomb, t{3,5,3}, , has alternating dodecahedron and icosidodecahedron cells, with a triangular prism vertex figure: There are four rectified compact regular honeycombs: The truncated icosahedral honeycomb, t{3,5,3}, , has alternating dodecahedron and truncated icosahedron cells, with a triangular pyramid vertex