Order-7 truncated triangular tiling

Order-7 truncated triangular tiling
Poincaré_disk_model
Type	Hyperbolic semiregular tiling
Vertex figure	7.6.6
Schläfli symbol	t{3,7}
Wythoff symbol	2 7 | 3
Coxeter-Dynkin
Symmetry	[7,3]
Dual	Order-3 heptakis heptagonal tiling
Properties	Vertex-transitive

In geometry, the Order 7 truncated heptagonal tiling, sometimes called the hyperbolic soccerball, is a semiregular tiling of the hyperbolic plane. There are two hexagons and one heptagon on each vertex, forming a pattern similar to a conventional soccer ball (truncated icosahedron) with heptagons in place of pentagons. It has Schläfli symbol of t_1,2{7,3}.

Dual tiling

The dual tiling is called an order-3 heptakis heptagonal tiling, named for being constructible as an order-3 heptagonal tiling with every heptagon divided into seven triangles by the center point.

See also

• Triangular tiling
• Order-3 heptagonal tiling
• Order-7 triangular tiling
• Tilings of regular polygons
• List of uniform tilings

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
• The Beauty of Geometry: Twelve Essays (1999), Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8 (Chapter 10: Regular honeycombs in hyperbolic space)

External links

• Weisstein, Eric W., "Hyperbolic tiling" from MathWorld.
• Weisstein, Eric W., "Poincaré hyperbolic disk" from MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch
• PDF with instructions
• The first paper hyperbolic soccerball
• A rather large hyperbolic soccerball