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
Cubic-octahedral honeycomb There are 5 related uniform honeycombs generated within the same family, generated with 2 or more rings of the Coxeter group : , , , , . The rectified cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from cuboctahedron, and rhombicuboctahedron cells, in a cuboid vertex figure. It has a Coxeter diagram . The cyclotruncated cubic-octahedral honeycomb is a compact uniform honeycomb, constructed from truncated cube, octahedron cells, in a square antiprism vertex figure. It has a Coxeter diagram . It can be seen as somewhat analogous to the trioctagonal tiling with truncated square and triangle facets: The cyclotruncated octahedral-cubic