Trigonal trapezohedral honeycomb 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 the "trigonal trapezohedral honeycomb". A different orthogonal projection produces the quadrille where the rhombi are distorted
5-demicubic honeycomb for n≥5) and it Voronoi tessellation is a tritruncated 5-cubic honeycomb, , containing all with bitruncated 5-orthoplex, Voronoi cells. There are three uniform construction symmetries of this tessellation. Each symmetry can be represented by arrangements of different colors on the 32 5-demicube facets around each vertex. Regular and uniform honeycombs in 5-space: 5-demicubic honeycomb The 5-demicube honeycomb, or demipenteractic honeycomb is a uniform space-filling tessellation (or honeycomb) in Euclidean 5-space. It is constructed as an alternation of the regular 5-cube honeycomb. It is the first tessellation in the demihypercube honeycomb family which, with all the next ones, is not regular,