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
Order-4 dodecahedral honeycomb truncated octahedron and truncated icosahedron cells, with a tetrahedron vertex figure. The cantellated order-4 dodecahedral honeycomb, has rhombicosidodecahedron and cuboctahedron, and cube cells, with a triangular prism vertex figure. The cantitruncated order-4 dodecahedral honeycomb, is a uniform honeycomb constructed with a coxeter diagram, and mirrored sphenoid vertex figure. The runcititruncated order-4 dodecahedral honeycomb, is a uniform honeycomb constructed with a coxeter diagram, and a quadrilateral pyramid vertex figure. Order-4 dodecahedral honeycomb In the geometry of hyperbolic 3-space, the order-4 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs). With Schläfli symbol {5,3,4}, it has four dodecahedra around