Rhombitetraheptagonal tiling
In today's world, Rhombitetraheptagonal tiling has taken on great relevance in various areas. Whether in the political, social, cultural or technological sphere, Rhombitetraheptagonal tiling has positioned itself as a central topic of debate and interest. Its impact has been noted in people's daily lives, as well as in the dynamics of societies and the evolution of different industries. In this article, we will explore the meaning and importance of Rhombitetraheptagonal tiling today, as well as its influence on different aspects of our lives. Furthermore, we will analyze how Rhombitetraheptagonal tiling continues to be a reference point in the contemporary world and how its relevance will continue to increase in the future.
| Rhombitetraheptagonal tiling | |
|---|---|
 Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 4.4.7.4 |
| Schläfli symbol | rr{7,4} or |
| Wythoff symbol | 4 | 7 2 |
| Coxeter diagram |    
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| Symmetry group | , (*742) |
| Dual | Deltoidal tetraheptagonal tiling |
| Properties | Vertex-transitive |
In geometry, the rhombitetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of rr{4,7}. It can be seen as constructed as a rectified tetraheptagonal tiling, r{7,4}, as well as an expanded order-4 heptagonal tiling or expanded order-7 square tiling.
Dual tiling
The dual is called the deltoidal tetraheptagonal tiling with face configuration V.4.4.4.7.
Related polyhedra and tiling
| *n42 symmetry mutation of expanded tilings: n.4.4.4 | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry , (*n42) |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | |||||||
| *342 |
*442 |
*542 |
*642 |
*742 |
*842 |
*∞42 | |||||
| Expanded figures |
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| 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 | ||||
| Uniform heptagonal/square tilings | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: , (*742) | +, (742) | , (7*2) | , (*772) | ||||||||
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| {7,4} | t{7,4} | r{7,4} | 2t{7,4}=t{4,7} | 2r{7,4}={4,7} | rr{7,4} | tr{7,4} | sr{7,4} | s{7,4} | h{4,7} | ||
| Uniform duals | |||||||||||
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| V74 | V4.14.14 | V4.7.4.7 | V7.8.8 | V47 | V4.4.7.4 | V4.8.14 | V3.3.4.3.7 | V3.3.7.3.7 | V77 | ||
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
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
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