Truncated order-6 pentagonal tiling
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| Truncated order-6 pentagonal tiling | |
|---|---|
| Truncated order-6 pentagonal tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 6.10.10 |
| Schläfli symbol | t{5,6} t(5,5,3) |
| Wythoff symbol | 2 6 | 5 3 5 5 | |
| Coxeter diagram | File:CDel node.pngFile:CDel 6.pngFile:CDel node 1.pngFile:CDel 5.pngFile:CDel node 1.png File:CDel branch 11.pngFile:CDel split2-55.pngFile:CDel node 1.png |
| Symmetry group | [6,5], (*652) [(5,5,3)], (*553) |
| Dual | Order-5 hexakis hexagonal tiling |
| Properties | Vertex-transitive |
In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.
Uniform colorings
| File:H2 tiling 355-7.png t012(5,5,3) |
File:H2 tiling 355-7-mirrors.png With mirrors |
| An alternate construction exists from the [(5,5,3)] family, as the omnitruncation t012(5,5,3). It is shown with two (colors) of decagons. | |
Symmetry
The dual of this tiling represents the fundamental domains of the *553 symmetry. There are no mirror removal subgroups of [(5,5,3)], but this symmetry group can be doubled to 652 symmetry by adding a bisecting mirror to the fundamental domains.
| Type | Reflective domains | Rotational symmetry |
|---|---|---|
| Index | 1 | 2 |
| Diagram | File:553 symmetry 000.png | File:553 symmetry aaa.png |
| Coxeter (orbifold) |
[(5,5,3)] = File:CDel node c1.pngFile:CDel split1-55.pngFile:CDel branch c1.png (*553) |
[(5,5,3)]+ = File:CDel node h2.pngFile:CDel split1-55.pngFile:CDel branch h2h2.png (553) |
Related polyhedra and tiling
| File:H2 tiling 355-1.png | File:H2 tiling 355-2.png | File:H2 tiling 355-3.png | File:H2 tiling 355-4.png | File:H2 tiling 355-5.png | File:H2 tiling 355-6.png | File:H2 tiling 355-7.png |
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.
See also
Wikimedia Commons has media related to Uniform tiling 6-10-10.
