Hexagonal tiling honeycomb
|Hexagonal tiling honeycomb|
|Bowers style acronym||Hexah|
|Coxeter diagram||x6o3o3o ()|
|Cells||2N hexagonal tilings|
|Vertex figure||Tetrahedron, edge length √|
|Measures (edge length 1)|
|Petrie dual||Petrial hexagonal tiling honeycomb|
|Abstract & topological properties|
The hexagonal tiling honeycomb, also known as the order-3 hexagonal tiling honeycomb, is a paracompact regular tiling of 3D hyperbolic space. Each cell is a hexagonal tiling whose vertices lie on a horosphere, a surface in hyperbolic space that approaches a single ideal point at infinity. 3 hexagonal tilings meet at each edge, and 4 meet at each vertex.
This honeycomb can be alternated into an alternated hexagonal tiling honeycomb, which is uniform.
Representations[edit | edit source]
The hexagonal tiling honeycomb has the following Coxeter diagrams:
- x6o3o3o () (full symmetry)
- x3x6o3o () (as truncated triangular tiling honeycomb)
- o6x3x6o () (as bitruncated order-6 hexagonal tiling honeycomb)
- o6x3x3x3*b () (half symmetry of bitruncated order-6 hexagonal tiling honeycomb)
- x3x3x3x3*a3*c *b3*d () (quarter symmetry of bitruncated order-6 hexagonal tiling honeycomb)
Related polytopes[edit | edit source]
[edit | edit source]
- Klitzing, Richard. "hexah".
- Wikipedia Contributors. "Hexagonal tiling honeycomb".
- lllllllllwith10ls. "Category 1: Regulars" (#5).