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
Order-6 hexagonal tiling honeycomb fundamental domain. It has an octahedral Coxeter diagram with 6 order-3 branches, and 3 infinite-order branches in the shape of a triangular prism, . It is one of 15 regular hyperbolic honeycombs in 3-space, 11 of which like this one are paracompact, with infinite cells or vertex figures. There are nine uniform honeycombs in the [6,3,6] Coxeter group family, including this regular form. It has a related alternation honeycomb, represented by ↔ , having alternating triangular tiling cells, and a regular form as , called a triangular tiling honeycomb. This honeycomb is a part of a sequence of polychora and