Hyperbolic great cubic honeycomb
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| Great cubic honeycomb | |
|---|---|
| (No image) | |
| Schläfli symbol | {4,3,5} |
| Type | Hyperbolic regular honeycomb |
| Cells | cube {4,3} |
| Faces | square {4} |
| Edge figure | pentagon {5} |
| Vertex figure | icosahedron {3,5} |
| Cells/edge | {4,3}5 |
| Cells/vertex | {4,3}20 |
| Euler characteristic | 0 |
| Symmetry group | group [4,3,5] |
| Dual | Small dodecahedral honeycomb {5,3,4} |
| Properties | Regular |
The great cubic honeycomb is the one of four space-filling tessellation (or honeycomb) in hyperbolic 3-space.
Five cubes exist on each edge, and 20 cubes around each vertex. It is dual with the hyperbolic small dodecahedral honeycomb.
It is related to the regular cubic honeycomb of Euclidean 3-space, which has 4 cubes per edge, and also the hypercube of Euclidean 4-space with 3 cubes per edge.
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