Tetrahedral-octahedral honeycomb
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| Tetrahedral-octahedral honeycomb | |
|---|---|
| Image:Tetrahedral-octahedral honeycomb.png | |
| Schläfli symbol | h{4,3,4} |
| Type | Uniform honeycomb |
| Cell types | {3,3}, {3,4} |
| Face types | triangle {3} |
| Edge figure | [{3,3}.{3,4}]2 (rectangle) |
| Vertex figure | 8 {3,3} 6 {3,4} (cuboctahedron) |
| Cells/edge | [{3,3}.{3,4}]2 |
| Faces/edge | 4 {3} |
| Cells/vertex | {3,3}8+{3,4}6 |
| Faces/vertex | 24 {3} |
| Edges/vertex | 12 |
| Symmetry group | Fm3m |
| Dual | rhombic dodecahedral honeycomb |
| Properties | vertex-uniform, edge-uniform, face-uniform |
The tetrahedral-octahedral honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of alternating tetrahedra and octahedra.
It is vertex-uniform with 8 tetrahedra and 6 octahedra around each vertex. It is edge-uniform with 2 tetrahedra and 2 octahedra alterating on each edge.
It can also be called an alternated cubic honeycomb because it can be constructed by starting with a cubic honeycomb and removing alternating adjacent vertices. This causes the cubic cells to degenerate into tetrahedral cells, and the voids created from the deleted vertices create octahedral cells. (It can be represented by an extended Schläfli symbol h{4,3,4} for containing half the vertices of the {4,3,4} cubic honeycomb.)
There's a similar honeycomb called gyrated tetrahedral-octahedral honeycomb which has layers rotated 90 degrees so half the edges have neighboring rather than alternating tetrahedra and octahedra.
[edit] See also
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