Octahedral honeycomb
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Octahedral honeycomb | |
---|---|
Rank | 4 |
Type | Regular, paracompact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Octh |
Coxeter diagram | o4o4o3x () |
Schläfli symbol | {3,4,4} |
Elements | |
Cells | NM octahedra |
Faces | 4NM triangles |
Edges | 3NM |
Vertices | 6N |
Vertex figure | Square tiling, edge length 1 |
Measures (edge length 1) | |
Circumradius | 0 |
Related polytopes | |
Army | Octh |
Regiment | Octh |
Dual | Square tiling honeycomb |
Abstract & topological properties | |
Orientable | Yes |
Properties | |
Symmetry | [4,4,3] |
Convex | Yes |
The order-4 octahedral honeycomb, or just octahedral honeycomb, is a paracompact regular tiling of 3D hyperbolic space. 4 ideal octahedra meet at each edge. All vertices are ideal points at infinity, with infinitely many octahedra meeting at each vertex in a square tiling arrangement.
Representations[edit | edit source]
The octahedral honeycomb has the following Coxeter diagrams:
- o4o4o3x () (full symmetry)
- o4o4o *b3x () (octahedra of two types)
- o3x3o4o4*a () (octahedra of three types, small rhombated square tiling verf)
- x3oØo3*a3oØo3*a () (octahedra of four types, diapeirogonal-diapeirogonal duocomb verf)
External links[edit | edit source]
- Klitzing, Richard. "octh".
- Wikipedia contributors. "Order-4 octahedral honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#14).