Bitruncated cubic honeycomb
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| Bitruncated cubic honeycomb | |
|---|---|
 |
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| Type | Uniform honeycomb |
| Cell type | (4.6.6) |
| Face types | square {4} hexagon {6} |
| Edge figure | isosceles triangle {3} |
| Vertex figure | 4 (4.6.6) (disphenoid tetrahedron) |
| Cells/edge | (4.6.6)3 |
| Cells/vertex | (4.6.6)4 |
| Faces/edge | 4.6.6 |
| Faces/vertex | 42.64 |
| Edges/vertex | 4 |
| Symmetry group | Im3m |
| Dual | Disphenoid tetrahedral honeycomb |
| Properties | cell-uniform, edge-uniform, vertex-uniform |
The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra.
It is one of 28 uniform honeycombs. It has 4 truncated octahedra around each vertex.
Being composed entirely of truncated octahedron, it is cell-uniform. It is also edge-uniform, with 2 hexagons and one square on each edge.
The honeycomb has two sources of truncated octahedra. Half are centered on the original cells of a cubic honeycomb, and half are centered on the vertices of the original honeycomb.
Although a regular tetrahedron can not tessellate space alone, the dual of this honeycomb has identical tetrahedral cells with isosceles triangle faces (called a disphenoid tetrahedron) and these do tessellate space. The dual of this honeycomb is the disphenoid tetrahedral honeycomb.
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