Order-∞ pentagonal tiling
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| Order-∞ pentagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular, paracompact |
| Space | Hyperbolic |
| Notation | |
| Bowers style acronym | Azpat |
| Coxeter diagram | o∞o5x (    ) |
| Schläfli symbol | {5,∞} |
| Elements | |
| Faces | 2NM pentagons |
| Edges | 5NM |
| Vertices | 10N |
| Vertex figure | Apeirogon, edge length (1+√5)/2 |
| Measures (edge length 1) | |
| Circumradius | |
| Related polytopes | |
| Army | Azpat |
| Regiment | Azpat |
| Dual | Order-5 apeirogonal tiling |
| Topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | [∞,5] |
| Convex | Yes |
The order-∞ pentagonal tiling or infinite-order pentagonal tiling is a paracompact regular tiling of the hyperbolic plane. Infinitely many ideal pentagons join at each vertex. All vertices are ideal points at infinity.
Representations[edit | edit source]
An order–∞ pentagonal tiling has the following Coxeter diagrams:
- o∞o5x (full symmetry)
- o5x5o∞*a (pentagons of two types)
Related polytopes[edit | edit source]
| Name | OBSA | Schläfli symbol | CD diagram | Picture |
|---|---|---|---|---|
| Order-5 apeirogonal tiling | pazat | {∞,5} |
|
 |
| Truncated order-5 apeirogonal tiling | topazat | t{∞,5} |
|
 |
| Pentaapeirogonal tiling | pazt | r{∞,5} |
|
 |
| Truncated order-∞ pentagonal tiling | tazpat | t{5,∞} |
|
 |
| Order-∞ pentagonal tiling | azpat | {5,∞} |
|
|
| Small rhombipentaapeirogonal tiling | sropazt | rr{∞,5} |
|
 |
| Great rhombipentaapeirogonal tiling | gropazt | tr{∞,5} |
|
 |
| Snub pentaapeirogonal tiling | sr{∞,5} | 
|
 |
External links[edit | edit source]
- Wikipedia Contributors. "Infinite-order pentagonal tiling".