Order-5 cubic honeycomb

It has a radical subgroup symmetry construction with dodecahedral fundamental domains: Coxeter notation: [4,(3,5)*], index 120.

The rectified order-5 cubic honeycomb, , has alternating icosahedron and cuboctahedron cells, with a pentagonal prism vertex figure.

The cantellated order-5 cubic honeycomb, , has rhombicuboctahedron, icosidodecahedron, and pentagonal prism cells, with a wedge vertex figure.

It is similar to the Euclidean (order-4) cantellated cubic honeycomb, rr{4,3,4}: The cantitruncated order-5 cubic honeycomb, , has truncated cuboctahedron, truncated icosahedron, and pentagonal prism cells, with a mirrored sphenoid vertex figure.

The omnitruncated order-5 cubic honeycomb or omnitruncated order-4 dodecahedral honeycomb, , has truncated icosidodecahedron, truncated cuboctahedron, decagonal prism, and octagonal prism cells, with an irregular tetrahedral vertex figure.

It has dodecahedron, rhombicosidodecahedron, and tetrahedron cells, with a triangular frustum vertex figure.

It is analogous to the 2D hyperbolic order-5 square tiling , {4,5}
It can be seen as analogous to the 2D hyperbolic tetrapentagonal tiling , r{4,5} with square and pentagonal faces