Order-6 hexagonal tiling honeycomb . The "cantellated order-6 hexagonal tiling honeycomb", t{6,3,6}, has trihexagonal tiling and rhombitrihexagonal tiling cells, with a triangular prism vertex figure. The "cantitruncated order-6 hexagonal tiling honeycomb", t{6,3,6}, has hexagonal tiling and truncated trihexagonal tiling cells, with a triangular prism vertex figure. The runcinated order-6 hexagonal tiling honeycomb, t{6,3,6}, has hexagonal tiling and hexagonal prism cells, with a triangular antiprism vertex figure. It is analogous to the 2D hyperbolic rhombihexahexagonal tiling, rr{6,6}, with square and hexagonal faces: The runcitruncated order-6 hexagonal tiling honeycomb, t{6,3,6}, has Truncated hexagonal tiling, rhombitrihexagonal tiling, hexagonal prism, and dodecagonal prism cells. The omnitruncated order-6 hexagonal
Cubic honeycomb <HR> The dual of the "cantellated cubic honeycomb" is called a quarter oblate octahedrille, a catoptric tessellation with Coxeter diagram , containing faces from two of four hyperplanes of the cubic [4,3,4] fundamental domain. It has irregular triangle bipyramid cells which can be seen as 1/12 of a cube, made from the cube center, 2 face centers, and 2 vertices. The cantitruncated cubic honeycomb or cantitruncated cubic cellulation is a uniform space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of truncated cuboctahedra, truncated octahedra, and cubes in a ratio of 1:1:3. John Horton Conway calls this honeycomb a n-tCO-trille,