Order-4 dodecahedral honeycomb and order-4 hexagonal tiling honeycomb all which have octahedral vertex figures: This honeycomb is a part of a sequence of polychora and honeycombs with dodecahedral cells: The rectified order-4 dodecahedral honeycomb, , has alternating octahedron and icosidodecahedron cells, with a cube vertex figure. There are four rectified compact regular honeycombs: The truncated order-4 dodecahedral honeycomb, , has octahedron and truncated dodecahedron cells, with a cube vertex figure. It can be seen as analogous to the 2D hyperbolic truncated order-4 pentagonal tiling, t{5,4} with truncated pentagon and square faces: The bitruncated order-4 dodecahedral honeycomb, or bitruncated order-5 cubic honeycomb, , has
Dodecahedral-icosahedral honeycomb Dodecahedral-icosahedral honeycomb In the geometry of hyperbolic 3-space, the dodecahedral-icosahedral honeycomb is a uniform honeycomb, constructed from dodecahedron, icosahedron, and icosidodecahedron cells, in a rhombicosidodecahedron vertex figure. Wide-angle perspective views: There are 5 related uniform honeycombs generated within the same family, generated with 2 or more rings of the Coxeter group : , , , , . The rectified dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from icosidodecahedron, and rhombicosidodecahedron cells, in a cuboid vertex figure. It has a Coxeter diagram . The cyclotruncated dodecahedral-icosahedral honeycomb is a compact uniform honeycomb, constructed from truncated dodecahedron, icosahedron cells, in a