Rectified octahedral honeycomb
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Rectified octahedral honeycomb | |
---|---|
Rank | 4 |
Type | Uniform, paracompact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Rocth |
Coxeter diagram | o4o4x3o () |
Elements | |
Cells | NM cuboctahedra, 6N square tilings |
Faces | 4NM triangles, 6NM squares |
Edges | 12NM |
Vertices | 3NM |
Vertex figure | Square prism, edge lengths √2 (base) and 1 (side) 75px |
Measures (edge length 1) | |
Circumradius | i |
Related polytopes | |
Army | Rocth |
Regiment | Rocth |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | [4,4,3] |
Convex | Yes |
The rectified octahedral honeycomb is a paracompact quasiregular tiling of 3D hyperbolic space. 2 square tilings and 4 cuboctahedra meet at each vertex. It is paracompact because it has Euclidean square tiling cells. As the name suggests, it can be derived by rectification of the octahedral honeycomb.
Representatoins[edit | edit source]
A rectified octahedral honeycomb has the following Coxeter diagrams:
- o4o4x3o () (full symmetry)
- o4x4o *b3o () (half symmetry, cuboid verf)
- x3o3x4o4*a () (rectangular trapezoprism verf)
External links[edit | edit source]
- Wikipedia contributors. "Rectified octahedral honeycomb".
- lllllllllwith10ls. "Category 4: Square Rectates" (#103).