Rhombitetrapentagonal tiling
In geometry, the rhombitetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,2{4,5}.
| Rhombitetrapentagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 4.4.5.4 |
| Schläfli symbol | rr{5,4} or |
| Wythoff symbol | 5 2 |
| Coxeter diagram |     or   |
| Symmetry group | [5,4], (*542) |
| Dual | Deltoidal tetrapentagonal tiling |
| Properties | Vertex-transitive |
Dual tiling
The dual is called the deltoidal tetrapentagonal tiling with face configuration V.4.4.4.5.
Related polyhedra and tiling
| Uniform pentagonal/square tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [5,4], (*542) | [5,4]+, (542) | [5+,4], (5*2) | [5,4,1+], (*552) | ||||||||
|
|
|
|
|
|
|
 |
|
| ||
 |
 |
 |
 |
 |
|
 |
 |
 |
 | ||
| {5,4} | t{5,4} | r{5,4} | 2t{5,4}=t{4,5} | 2r{5,4}={4,5} | rr{5,4} | tr{5,4} | sr{5,4} | s{5,4} | h{4,5} | ||
| Uniform duals | |||||||||||
 |
|
|
|
|
|
|
 |
|
| ||
|
 |
 |
 |
|
 |
 |
 |
 | |||
| V54 | V4.10.10 | V4.5.4.5 | V5.8.8 | V45 | V4.4.5.4 | V4.8.10 | V3.3.4.3.5 | V3.3.5.3.5 | V55 | ||
| *n42 symmetry mutation of expanded tilings: n.4.4.4 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry [n,4], (*n42) |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | |||||||
| *342 [3,4] |
*442 [4,4] |
*542 [5,4] |
*642 [6,4] |
*742 [7,4] |
*842 [8,4] |
*∞42 [∞,4] | |||||
| Expanded figures |
 |
 |
|
 |
 |
 |
 | ||||
| Config. | 3.4.4.4 | 4.4.4.4 | 5.4.4.4 | 6.4.4.4 | 7.4.4.4 | 8.4.4.4 | ∞.4.4.4 | ||||
| Rhombic figures config. |
 V3.4.4.4 |
 V4.4.4.4 |
V5.4.4.4 |
 V6.4.4.4 |
 V7.4.4.4 |
 V8.4.4.4 |
 V∞.4.4.4 | ||||
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.
See also
 |
Wikimedia Commons has media related to Uniform tiling 4-4-4-5. |
External links
- Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- Hyperbolic and Spherical Tiling Gallery
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
- Hyperbolic Planar Tessellations, Don Hatch
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.