Great rhombitriheptagonal tiling

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Great rhombitriheptagonal tiling
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

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 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

• Tilings of regular polygons
• List of uniform planar tilings

[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