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
Cubic honeycomb cells.<br>Although it is not uniform, constructionally it can be given as Coxeter diagrams or . <HR> The runcic cantitruncated cubic honeycomb or runcic cantitruncated cubic cellulation contains cells: snub cubes, rhombicuboctahedrons, and cubes. In addition the gaps created at the alternated vertices form an irregular cell.<br>Although it is not uniform, constructionally it can be given as Coxeter diagram . <HR> The runcitruncated cubic honeycomb or runcitruncated cubic cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space. It is composed of rhombicuboctahedra, truncated cubes, octagonal prisms, and cubes in a ratio of 1:1:3:3. Its name is derived from its