Cubic honeycomb
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| Cubic honeycomb | |
|---|---|
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| Schläfli symbol | {4,3,4} |
| Type | Regular honeycomb |
| Cell type | {4,3} |
| Face type | {4} |
| Vertex figure | 8 {4,3} (octahedron) |
| Cells/edge | {4,3}4 |
| Faces/edge | 44 |
| Cells/vertex | {4,3}8 |
| Faces/vertex | 412 |
| Edges/vertex | 6 |
| Euler characteristic | 0 |
| Symmetry group | group [4,3,4] |
| Dual | self-dual |
| Properties | Regular, vertex-uniform |
The cubic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space. It is an analog of the square tiling of the plane.
It is one of 28 uniform honeycombs using regular and semiregular polyhedral cells.
Four cubes exist on each edge, and 8 cubes around each vertex. It is a self-dual tessellation.
It is related to the regular tesseract (hypercube) which exists in 4-space with 3 cubes on each edge.
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