| Infinite-order pentagonal tiling | |
|---|---|
 Poincaré disk model of thehyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 5∞ |
| Schläfli symbol | {5,∞} |
| Wythoff symbol | ∞ | 5 2 |
| Coxeter diagram |        |
| Symmetry group | [∞,5], (*∞52) |
| Dual | Order-5 apeirogonal tiling |
| Properties | Vertex-transitive,edge-transitive,face-transitive |
In 2-dimensionalhyperbolic geometry, theinfinite-order pentagonal tiling is aregular tiling. It hasSchläfli symbol of {5,∞}. All vertices areideal, located at "infinity", seen on the boundary of thePoincaré hyperbolic disk projection.
There is a half symmetry form,, seen with alternating colors:
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).
| Finite | Compact hyperbolic | Paracompact | ||||
|---|---|---|---|---|---|---|
 {5,3}  |  {5,4}  |  {5,5} |  {5,6}  |  {5,7}  |  {5,8}...  | {5,∞} |
| Paracompact uniform apeirogonal/pentagonal tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [∞,5], (*∞52) | [∞,5]+ (∞52) | [1+,∞,5] (*∞55) | [∞,5+] (5*∞) | ||||||||
| | | | | | |  |  | | | |
 |  |  |  | |  |  |  |  | |||
| {∞,5} | t{∞,5} | r{∞,5} | 2t{∞,5}=t{5,∞} | 2r{∞,5}={5,∞} | rr{∞,5} | tr{∞,5} | sr{∞,5} | h{∞,5} | h2{∞,5} | s{5,∞} | |
| Uniform duals | |||||||||||
 | | | | | | |  | | | | |
 |  | |  | ||||||||
| V∞5 | V5.∞.∞ | V5.∞.5.∞ | V∞.10.10 | V5∞ | V4.5.4.∞ | V4.10.∞ | V3.3.5.3.∞ | V(∞.5)5 | V3.5.3.5.3.∞ | ||
