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},
Order-5 cubic honeycomb and pentagonal prism cells, with an octahedron vertex figure. It is analogous to the 2D hyperbolic rhombitetrapentagonal tiling, rr{4,5}, with square and pentagonal faces: It is similar to the Euclidean (order-4) runcinated cubic honeycomb, t{4,3,4}: The runcitruncated order-5 cubic honeycomb or runcicantellated order-4 dodecahedral honeycomb , has cube, dodecahedron, and pentagonal prism cells, with a quad-pyramid vertex figure. It is similar to the Euclidean (order-4) runcitruncated cubic honeycomb, t{4,3,4}: The omnitruncated order-5 cubic honeycomb or omnitruncated order-4 dodecahedral honeycomb has Coxeter diagram . It is similar to the Euclidean (order-4) omnitruncated cubic honeycomb, t{4,3,4}: In 3-dimensional hyperbolic geometry, the alternated