Great rhombi-tetrahedral-octahedral honeycomb
(Redirected from Great rhombated tetrahedral-octahedral honeycomb)
Great rhombi-tetrahedral-octahedral honeycomb | |
---|---|
Rank | 4 |
Type | uniform |
Space | Euclidean |
Notation | |
Bowers style acronym | Gratoh |
Coxeter diagram | x3x3o *b4x () |
Elements | |
Cells | 2N truncated tetrahedra, N truncated cubes, N great rhombicuboctahedra |
Faces | 8N triangles, 6N squares, 8N hexagons, 6N octagons |
Edges | 12N+12N+24N |
Vertices | 24N |
Vertex figure | Sphenoid, edge lengths 1 (1), √2 (1), √3 (2), and √2+√2 (2) |
Measures (edge length 1) | |
Vertex density | |
Dual cell volume | |
Related polytopes | |
Army | Gratoh |
Regiment | Gratoh |
Dual | Half sphenoidal honeycomb |
Conjugate | Great quasirhombi-tetrahedral-octahedral honeycomb |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | S4 |
Convex | Yes |
Nature | Tame |
The great rhombi-tetrahedral-octahedral honeycomb, or gratoh, also known as the runcicantic cubic honeycomb, is a convex uniform honeycomb. 1 truncated tetrahedron, 1 truncated cube, and 2 great rhombicuboctahedra join at each vertex of this honeycomb. It can be formed as an alternated faceting from the prismatorhombated cubic honeycomb, or alternately as the bitruncation of the tetrahedral-octahedral honeycomb.
Representations[edit | edit source]
A great rhombated tetrahedral-octahedral honeycomb has the following Coxeter diagrams:
- x3x3o *b4x (full symmetry)
- s4o3x4x (as alternated faceting)
Gallery[edit | edit source]
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Wireframe
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External links[edit | edit source]
- Klitzing, Richard. "gratoh".
- Wikipedia contributors. "Runcicantic cubic honeycomb".
- Binnendyk, Eric. "Category 5: Greater Truncates" (#93).