Great rhombitriheptagonal tiling
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| Great rhombitriheptagonal tiling | |
|---|---|
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| Type | Uniform tiling |
| Vertex figure | 4.7.12 |
| Schläfli symbol |  or t0,1,2{7,3} |
| Wythoff symbol | 2 7 3 | |
| Coxeter-Dynkin |    |
| Symmetry | [7,3] |
| Dual | Order-3 bisected heptagonal tiling |
| Properties | Vertex-transitive |
 4.7.12 |
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In geometry, the Great rhombitrihexagonal tiling (or Omnitruncated trihexagonal tiling) is a semiregular tiling of the Euclidean plane. There are one square, one hexagon, and one tetrakaidecagon(14-sides) on each vertex. It has Schläfli symbol of t0,1,2{3,7}.
The image shows a Poincaré disk model projection of the hyperbolic plane.
This tiling is topologically related as a part of sequence of omnitruncated polyhedra with vertex figure (4.6.2n). This set of polyhedra are zonohedrons.
 (4.6.6) |
 (4.6.8) |
 (4.6.10) |
 (4.6.12) |
There is only one uniform colorings of an order-3 heptagonal tiling. (Naming the colors by indices around a vertex: 123.)
[edit] Dual tiling
The dual tiling is called an order-3 bisected heptagonal tiling, made as a complete bisection of the order-3 heptagonal tiling, here with triangles colored alternatingly white and blue.
Each triangle in this dual tiling represent a fundamental domain of the Wythoff construction for the symmetry group [7,3].
[edit] See also
[edit] External links
- Eric W. Weisstein, Hyperbolic tiling at MathWorld.
- Eric W. Weisstein, Poincare hyperbolic disk at 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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