Triangular tiling honeycomb The omnitruncated triangular tiling honeycomb, , has truncated trihexagonal tiling and hexagonal prism cells, with a tetrahedron vertex figure. The runcisnub triangular tiling honeycomb, , has trihexagonal tiling, triangular tiling, triangular prism, and triangular cupola cells. It is vertex-transitive, but not uniform, since it contains Johnson solid triangular cupola cells. Triangular tiling honeycomb The triangular tiling honeycomb is one of 11 paracompact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. It is called "paracompact" because it has infinite cells and vertex figures, with all vertices as ideal points at infinity. It has Schläfli symbol {3,6,3}, being composed of triangular tiling
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