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-5 cubic honeycomb t{4,5} with truncated square and pentagonal faces: It is similar to the Euclidean (order-4) truncated cubic honeycomb, t{4,3,4}, with octahedral cells at the truncated vertices. Same as Bitruncated order-4 dodecahedral honeycomb The cantellated order-5 cubic honeycomb, , has rhombicuboctahedron and icosidodecahedron cells, with a wedge vertex figure. It is similar to the Euclidean (order-4) cantellated cubic honeycomb, rr{4,3,4}: The cantitruncated order-5 cubic honeycomb, , has rhombicuboctahedron and icosidodecahedron cells, with a mirrored sphenoid vertex figure. It is similar to the Euclidean (order-4) cantitruncated cubic honeycomb, tr{4,3,4}: The runcinated order-5 cubic honeycomb or runcinated order-4 dodecahedral honeycomb , has cube, dodecahedron,