Order-5 pentagonal tiling
In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,5}, constructed from five pentagons around every vertex. As such, it is self-dual.
Order-5 pentagonal tiling | |
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Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 55 |
Schläfli symbol | {5,5} |
Wythoff symbol | 5 2 |
Coxeter diagram | |
Symmetry group | [5,5], (*552) |
Dual | self dual |
Properties | Vertex-transitive, edge-transitive, face-transitive |
Related tilings
Spherical | Hyperbolic tilings | |||||||
---|---|---|---|---|---|---|---|---|
{2,5} |
{3,5} |
{4,5} |
{5,5} |
{6,5} |
{7,5} |
{8,5} |
... | {∞,5} |
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,∞} |
Uniform pentapentagonal tilings | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Symmetry: [5,5], (*552) | [5,5]+, (552) | ||||||||||
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{5,5} | t{5,5} |
r{5,5} | 2t{5,5}=t{5,5} | 2r{5,5}={5,5} | rr{5,5} | tr{5,5} | sr{5,5} | ||||
Uniform duals | |||||||||||
V5.5.5.5.5 | V5.10.10 | V5.5.5.5 | V5.10.10 | V5.5.5.5.5 | V4.5.4.5 | V4.10.10 | V3.3.5.3.5 |
See also
Wikimedia Commons has media related to Order-5 pentagonal tiling. |
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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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