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Order-5 apeirogonal tiling
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In geometry, the order-5 apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,5}.
| Order-5 apeirogonal tiling | |
|---|---|
Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | ∞5 |
| Schläfli symbol | {∞,5} |
| Wythoff symbol | 5 | ∞ 2 |
| Coxeter diagram |     |
| Symmetry group | [∞,5], (*∞52) |
| Dual | Infinite-order pentagonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive edge-transitive |
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Symmetry
The dual to this tiling represents the fundamental domains of [∞,5*] symmetry, orbifold notation *∞∞∞∞∞ symmetry, a pentagonal domain with five ideal vertices.
The order-5 apeirogonal tiling can be uniformly colored with 5 colored apeirogons around each vertex, and coxeter diagram: 
, except ultraparallel branches on the diagonals.
Related polyhedra and tiling
This tiling is also topologically related as a part of sequence of regular polyhedra and tilings with five faces per vertex, starting with the icosahedron, with Schläfli symbol {n,5}, and Coxeter diagram 
, with n progressing to infinity.
See also
Wikimedia Commons has media related to Order-5 apeirogonal tiling.
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
External links
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