Icosahedral honeycomb figure. The bitruncated icosahedral honeycomb, t{3,5,3}, , has truncated dodecahedron cells with a disphenoid vertex figure. The cantellated icosahedral honeycomb, t{3,5,3}, , has rhombicosidodecahedron and icosidodecahedron cells, with a triangular prism vertex figure. The cantitruncated icosahedral honeycomb, t{3,5,3}, , has truncated icosidodecahedron, icosidodecahedron, triangular prism and hexagonal prism cells, with a mirrored sphenoid vertex figure. The runcinated icosahedral honeycomb, t{3,5,3}, , has icosahedron and triangular prism cells, with a pentagonal antiprism vertex figure. The runcitruncated icosahedral honeycomb, t{3,5,3}, , has truncated icosahedron, rhombicosidodecahedron, hexagonal prism and triangular prism cells, with a square pyramid vertex figure. The omnitruncated icosahedral honeycomb, t{3,5,3},
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