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-5 dodecahedral honeycomb The runcitruncated order-5 dodecahedral honeycomb, , has truncated dodecahedron, icosidodecahedron and pentagonal prism cells, with a distorted square pyramid vertex figure. The omnitruncated order-5 dodecahedral honeycomb, , has truncated icosidodecahedron and decagonal prism cells, with a disphenoid vertex figure. Order-5 dodecahedral honeycomb The order-5 dodecahedral honeycomb is one of four compact regular space-filling tessellations (or honeycombs) in hyperbolic 3-space. With Schläfli symbol {5,3,5}, it has five dodecahedral cells around each edge, and each vertex is surrounded by twenty dodecahedra. Its vertex figure is a regular icosahedron. The dihedral angle of a Euclidean regular dodecahedron is ~116.6°, so no more than