User:Notsam1/sandboxagain
In geometry, the order-7 pentagonal tiling is a regular tiling of the hyperbolic plane, which holds the Schläfli symbol of {5,7}, representing its dual, that is, the order-5 heptagonal tiling which holds the Schläfli symbol of {7,5}.
| Order-7 pentagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic regular tiling |
| Vertex configuration | 57 |
| Schläfli symbol | {5,7} |
| Wythoff symbol | 5 | 7 2 |
| Coxeter diagram |    
|
| Symmetry group | [5,7], (*572) |
| Dual | Order-5 heptagonal tiling |
| Properties | Vertex-transitive, edge-transitive, face-transitive |
Related polyhedra and tiling
[edit]| Finite | Compact hyperbolic | Paracompact | ||||
|---|---|---|---|---|---|---|
 {5,3} 
|
 {5,4} 
|
 {5,5}
|
 {5,6} 
|
{5,7}
|
 {5,8}... 
|
 {5,∞} 
|
This tiling is topologically related as a part of sequence of regular tilings with pentagonal faces,[1] starting with the pentagonal filing, holding the Schläfli symbol {5,n}, and Coxeter diagram 
, whereby n is progressing towards infinity.
See also
[edit]References
[edit]- 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.
- Weisstein, Eric (2007-08-07). "Making MathWorld". The Mathematica Journal. 10 (3). doi:10.3888/tmj.10.3-3. ISSN 1097-1610.
- "Hyperbolic Planar Tesselations". www.plunk.org. Retrieved 2025-01-03.
- Weisstein, Eric W. "Schläfli Symbol". MathWorld. Retrieved January 3, 2025.
- ^ "Hyperbolic Planar Tesselations". www.plunk.org. Retrieved 2025-01-03.
External links
[edit]- Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
- KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
