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 honeycomb omnitruncated cubic honeycomb orfull snub cubic honeycomb can be constructed by alternation of the omnitruncated cubic honeycomb, although it can not be made uniform, but it can be given Coxeter diagram: and has symmetry [[4,3,4]]. It makes snub cubes from the truncated cuboctahedra, square antiprisms from the octagonal prisms and with new tetrahedral cells created in the gaps. A dual alternated omnitruncated cubic honeycomb is a space-filling honeycomb constructed as the dual of the alternated omnitruncated cubic honeycomb. Cells can be seen from tetrahedra as 1/48 of a cube, augmented by new center point of adjacent tetrahedra. 24 cells fit