Trigonal trapezohedral honeycomb into squares. It is dual to the quarter cubic honeycomb with tetrahedral and truncated tetrahedral cells: Trigonal trapezohedral honeycomb The trigonal trapezohedral honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. Cells are identical trigonal trapezohedron or rhombohedra. John Horton Conway calls it an oblate cubille. This honeycomb can be seen as a rhombic dodecahedral honeycomb, with the rhombic dodecahedra dissected with its center into 4 trigonal trapezohedra or rhombohedra. It is analogous to the regular hexagonal being dissectable into 3 rhombi and tiling the plane as a rhombille. The rhombille tiling is actually an orthogonal projection of
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