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
Tetrahedral-octahedral honeycomb in 3 of 4 hyperplanes of the [4,3], formula_4 Coxeter group. Cells are irregular pyramids and can be seen as 1/12 of a cube, or 1/24 of a rhombic dodecahedron, each defined with three corner and the cube center. A related uniform skew apeirohedron exists with the same vertex arrangement, but triangles and square removed. It can be seen as truncated tetrahedra and truncated cubes augmented together. The gyrated tetrahedral-octahedral honeycomb or gyrated alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of octahedra and tetrahedra in a ratio of 1:2. It is vertex-uniform with