Dodecahedral-icosahedral honeycomb square antiprism vertex figure. It has a Coxeter diagram . The cyclotruncated icosahedral-dodecahedral honeycomb is a compact uniform honeycomb, constructed from dodecahedron, truncated icosahedron cells, in a triangular antiprism vertex figure. It has a Coxeter diagram . It can be see as somewhat analogous to the pentahexagonal tiling with pentagonal and hexagonal faces: The truncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated icosahedron, truncated dodecahedron, rhombicosidodecahedron, truncated icosidodecahedron cells, in a trapezoidal pyramid vertex figure. It has a Coxeter diagram . The omnitruncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated icosidodecahedron cells, in a
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