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},
Pentagrammic-order 600-cell honeycomb can also be constructed by taking the order-5 5-cell honeycomb and replacing clusters of 600 5-cells meeting at a vertex with 600-cells. Each 5-cell belongs to five such clusters, and thus the pentagrammic-order 600-cell honeycomb has density 5. Pentagrammic-order 600-cell honeycomb In the geometry of hyperbolic 4-space, the pentagrammic-order 600-cell honeycomb is one of four regular star-honeycombs. With Schläfli symbol {3,3,5,5/2}, it has five 600-cells around each face in a pentagrammic arrangement. It is dual to the small stellated 120-cell honeycomb. It can be considered the higher-dimensional analogue of the 4-dimensional icosahedral 120-cell and the 3-dimensional great dodecahedron. It is