Each cell consists of a hexagonal tiling whose vertices lie on a horosphere, a flat plane in hyperbolic space that approaches a single ideal point at infinity.
A lower-symmetry construction of index 120, [6,(3,5)*], exists with regular dodecahedral fundamental domains, and an icosahedral Coxeter-Dynkin diagram with 6 axial infinite-order (ultraparallel) branches.
It is a part of sequence of regular hyperbolic honeycombs of the form {6,3,p}, with hexagonal tiling facets: It is also part of a sequence of regular polychora and honeycombs with icosahedral vertex figures: The rectified order-5 hexagonal tiling honeycomb, t1{6,3,5}, has icosahedron and trihexagonal tiling facets, with a pentagonal prism vertex figure.
It is similar to the 2D hyperbolic infinite-order square tiling, r{∞,5} with pentagon and apeirogonal faces.
The runcitruncated order-5 hexagonal tiling honeycomb, t0,1,3{6,3,5}, has truncated hexagonal tiling, rhombicosidodecahedron, pentagonal prism, and dodecagonal prism cells, with an isosceles-trapezoidal pyramid vertex figure.
The omnitruncated order-5 hexagonal tiling honeycomb, t0,1,2,3{6,3,5}, has truncated trihexagonal tiling, truncated icosidodecahedron, decagonal prism, and dodecagonal prism facets, with an irregular tetrahedral vertex figure.