Gyrated tetrahedral-octahedral honeycomb
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| Gyrated tetrahedral-octahedral honeycomb | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Euclidean |
| Notation | |
| Bowers style acronym | Gytoh |
| Coxeter diagram |       |
| Elements | |
| Cells | 2N tetrahedra, N octahedra |
| Faces | N+N+6N triangles |
| Edges | 3N+3N |
| Vertices | N |
| Vertex figure | Triangular orthobicupola, edge length 1 |
| Related polytopes | |
| Army | Gytoh |
| Regiment | Gytoh |
| Dual | Rhombitrapezohedral dodecahedral honeycomb |
| Conjugate | None |
| Abstract & topological properties | |
| Orientable | Yes |
| Properties | |
| Symmetry | V3❘W2 |
| Convex | Yes |
The gyrated tetrahedral-octahedral honeycomb, also known as the gyrated alternated cubic honeycomb, is a convex uniform honeycomb. 6 octahedra and 8 tetrahedra join at each vertex of this honeycomb. It is also the alternated hexagonal prismatic honeycomb.
This honeycomb can be formed from the tetrahedral-octahedral honeycomb by gyrating alternate layers of cells, so that some tetrahedra join to other tetrahedra, and some octahedra connect to other octahedra. In the normal tetrahedral-octahedral honeycomb, triangles always join one tetrahedron and one octahedron. As a result, the tetrahedral-octahedral honeycomb's cuboctahedral vertex figure turns into a triangular orthobicupola, or gyrated cuboctahedron.
Gallery[edit | edit source]
Wireframe
External links[edit | edit source]
- Klitzing, Richard. "gytoh".
- Wikipedia Contributors. "Gyrated tetrahedral-octahedral honeycomb".