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
Cubic honeycomb projected into the euclidean plane with various symmetry arrangements. There is a second uniform coloring by reflectional symmetry of the Coxeter groups, the second seen with alternately colored truncated cubic cells. <HR> The alternated bitruncated cubic honeycomb or bisnub cubic honeycomb can be creating regular icosahedron from the truncated octahedra with irregular tetrahedral cells created in the gaps. There are three constructions from three related Coxeter diagrams: , , and . These have symmetry [4,3,4], [4,(3)] and [3] respectively. The first and last symmetry can be doubled as <nowiki></nowiki>4,3,4 and [[3]]. This honeycomb is represented in the boron atoms of