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 |
| 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)
- o6x6o∞*a (hexagons of two types)
Related polytopes[edit | edit source]
| Name | OBSA | Schläfli symbol | CD diagram | Picture |
|---|---|---|---|---|
| Order-6 apeirogonal tiling | hazat | {∞,6} |
|
 |
| Truncated order-6 apeirogonal tiling | thazat | t{∞,6} |
|
 |
| Hexaapeirogonal tiling | hazt | r{∞,6} |
|
 |
| Truncated order-∞ hexagonal tiling | tazhat | t{6,∞} |
|
 |
| Order-∞ hexagonal tiling | azhat | {6,∞} |
|
|
| Small rhombihexaapeirogonal tiling | srohazt | rr{∞,6} |
|
 |
| Great rhombihexaapeirogonal tiling | grohazt | tr{∞,6} |
|
 |
| Snub hexaapeirogonal tiling | sr{∞,6} | 
|
 |
External links[edit | edit source]
- Wikipedia Contributors. "Infinite-order hexagonal tiling".