Great rhombitriheptagonal tiling

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Great rhombitriheptagonal tiling
Type	Uniform tiling
Vertex figure	4.6.14
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
4.6.14
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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 t_0,1,2{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 great rhombitrihexagonal tiling. (Naming the colors by indices around a vertex: 123.)

Contents 1 Dual tiling 2 References 3 See also 4 External links

[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] References

• Grünbaum, Branko; Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman and Company. ISBN 0-7167-1193-1. 

[edit] See also

• Tilings of regular polygons
• List of uniform planar tilings

[edit] External links

• Eric W. Weisstein, Hyperbolic tiling at MathWorld.
• Eric W. Weisstein, Poincaré 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