Order-6 dodecahedral honeycomb are on the ideal surface. 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 15 uniform honeycombs in the [5,3,6] Coxeter group family, including this regular form and its regular dual, order-5 hexagonal tiling honeycomb, {6,3,5}. This honeycomb is a part of a sequence of polychora and honeycombs with triangular tiling vertex figures: This honeycomb is a part of a sequence of regular polytopes and honeycombs with dodecahedral cells: The rectified order-6 dodecahedral honeycomb, t{5,3,6} has icosidodecahedron and triangular tiling cells connected in
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