Dodecahedral-icosahedral_honeycomb
In the geometry of hyperbolic 3-space, the dodecahedral-icosahedral honeycomb is a uniform honeycomb, constructed from dodecahedron, icosahedron, and icosidodecahedron cells, in a rhombicosidodecahedron vertex figure.
| Dodecahedral-icosahedral honeycomb | |
|---|---|
| Type | Compact uniform honeycomb |
| Schläfli symbol | {(3,5,3,5)} or {(5,3,5,3)} |
| Coxeter diagram |     or  |
| Cells | {5,3}  {3,5}  r{5,3}  |
| Faces | triangle {3} pentagon {5} |
| Vertex figure |  rhombicosidodecahedron |
| Coxeter group | [(5,3)[2]] |
| Properties | Vertex-transitive, edge-transitive |
A geometric honeycomb is a space-filling of polyhedral or higher-dimensional cells, so that there are no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions.
Honeycombs are usually constructed in ordinary Euclidean ("flat") space, like the convex uniform honeycombs. They may also be constructed in non-Euclidean spaces, such as hyperbolic uniform honeycombs. Any finite uniform polytope can be projected to its circumsphere to form a uniform honeycomb in spherical space.
