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},
24-cell honeycomb 24-cell honeycomb In four-dimensional Euclidean geometry, the 24-cell honeycomb, or icositetrachoric honeycomb is a regular space-filling tessellation (or honeycomb) of 4-dimensional Euclidean space by regular 24-cells. It can be represented by Schläfli symbol {3,4,3,3}. The dual tessellation by regular 16-cell honeycomb has Schläfli symbol {3,3,4,3}. Together with the tesseractic honeycomb (or 4-cubic honeycomb) these are the only regular tessellations of Euclidean 4-space. If a 3-sphere is inscribed in each hypercell of this tessellation, the resulting arrangement is the densest possible regular sphere packing in four dimensions, with the kissing number 24. The packing density of this arrangement is The 24-cell