Apeirogonal tiling
(Redirected from Order-3 apeirogonal tiling)
| Apeirogonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Azat |
| Coxeter diagram | x∞o3o (    ) |
| Schläfli symbol | {∞,3} |
| Elements | |
| Faces | 6N apeirogons |
| Edges | 3NM |
| Vertices | 2NM |
| Vertex figure | Triangle, edge length 2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Azat |
| Regiment | Azat |
| Dual | Order-∞ triangular tiling |
| Abstract & topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [∞,3] |
| Convex | Yes |
The order-3 apeirogonal tiling, or just apeirogonal tiling or azat, is a paracompact regular tiling of the hyperbolic plane. 3 apeirogons join at each vertex.
It can be formed by truncating the order-∞ apeirogonal tiling.
Representations[edit | edit source]
The apeirogonal tiling has the following Coxeter diagrams:
- x∞o3o () (full symmetry)
- x∞x∞o () (as truncated order-∞ apeirogonal tiling)
- x∞x∞x∞*a (
) (three types of faces)
External links[edit | edit source]
- Klitzing, Richard. "azat".
- Wikipedia contributors. "Order-3 apeirogonal tiling".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Apeirogonal tiling | azat | {∞,3} | |  |
| Triapeirogonal tiling | tazt | r{∞,3} | |  |
| Order-∞ triangular tiling | aztrat | {3,∞} | |  |
| Truncated apeirogonal tiling | tazat | t{∞,3} | |  |
| Small rhombitriapeirogonal tiling | srotazt | rr{∞,3} | |  |
| Truncated order-∞ triangular tiling | taztrat | t{3,∞} | |  |
| Great rhombitriapeirogonal tiling | grotazt | tr{∞,3} | |  |
| Snub triapeirogonal tiling | sr{∞,3} |  |  | |
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Order-∞ apeirogonal tiling | azazat | {∞,∞} | |  |
| Apeiroapeirogonal tiling = Order-4 apeirogonal tiling | squazat | r{∞,∞} | |  |
| Order-∞ apeirogonal tiling | azazat | {∞,∞} | |  |
| Truncated order-∞ apeirogonal tiling = Apeirogonal tiling | azat | t{∞,∞} | |  |
| Small rhombiapeiroapeirogonal tiling = Tetraapeirogonal tiling | tezt | rr{∞,∞} | |  |
| Truncated order-∞ apeirogonal tiling = Apeirogonal tiling | azat | t{∞,∞} | |  |
| Great rhombiapeiroapeirogonal tiling = Truncated order-4 apeirogonal tiling | tosquazat | tr{∞,∞} | |  |
| Snub apeiroapeirogonal tiling | sr{∞,∞} | |  | |