Order-∞ hexagonal tiling
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Order-∞ hexagonal tiling | |
---|---|
Rank | 3 |
Type | Regular, paracompact |
Space | Hyperbolic |
Notation | |
Bowers style acronym | Azhexat |
Coxeter diagram | o∞o6x () |
Schläfli symbol | {6,∞} |
Elements | |
Faces | NM hexagons |
Edges | 3NM |
Vertices | 6N |
Vertex figure | Apeirogon, edge length √3 |
Measures (edge length 1) | |
Circumradius | |
Related polytopes | |
Army | Azhexat |
Regiment | Azhexat |
Dual | Order-6 apeirogonal tiling |
Abstract & topological properties | |
Surface | Sphere |
Orientable | Yes |
Genus | 0 |
Properties | |
Symmetry | [∞,6] |
Convex | Yes |
The order-∞ hexagonal tiling or infinite-order hexagonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal hexagons join at each vertex. All vertices are ideal points at infinity.
Representations[edit | edit source]
An order–∞ hexagonal tiling has the following Coxeter diagrams:
- o∞o6x () (full symmetry)
- x6o∞o6*a () (hexagons of two types)
External links[edit | edit source]
- Wikipedia contributors. "Infinite-order hexagonal tiling".