Triangular tiling honeycomb
|Triangular tiling honeycomb|
|Bowers style acronym||Trah|
|Coxeter diagram||x3o6o3o ()|
|Cells||NM triangular tilings|
|Vertex figure||Hexagonal tiling, edge length 1|
|Measures (edge length 1)|
|Dual||Triangular tiling honeycomb|
|Abstract & topological properties|
The order-3 triangular tiling honeycomb, or just triangular tiling honeycomb, is a paracompact regular tiling of 3D hyperbolic space. 3 ideal triangular tilings meet at each edge. All vertices are ideal points at infinity, with infinitely many triangular tilings meeting at each vertex in a hexagonal tiling arrangement.
Representations[edit | edit source]
The triangular tiling honeycomb has the following Coxeter diagrams:
- x3o6o3o () (full symmetry)
- o6o3x3o3*b () (cells of two types, truncated tiangular tiling verf)
- x3o3o3o3*a3*c *b3*d () (cells of three types)
[edit | edit source]
- Klitzing, Richard. "trah".
- Wikipedia Contributors. "Triangular tiling honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#12).