Order-3 snub heptagonal tiling

Order-3 snub heptagonal tiling
Poincaré_disk_model
Type	Hyperbolic semiregular tiling
Vertex figure	3.3.3.3.7
Schläfli symbol	s{7,3}
Wythoff symbol	| 7 3 2
Coxeter-Dynkin
Symmetry	[7,3]
Dual	Order-7-3 floret pentagonal tiling
Properties	Vertex-transitive Chiral

In geometry, the order-3 snub heptagonal tiling is a semiregular tiling of the hyperbolic plane. There are four triangles, one heptagon on each vertex. It has Schläfli symbol of s{7,3}.

Related polyhedra and tilings

This tiling is part of sequence of snubbed polyhedra with vertex figure (3.3.3.3.p) and Coxeter-Dynkin diagram . These face-transitive figures have (n32) rotational symmetry.

(3.3.3.3.3) (332)	(3.3.3.3.4) (432)	(3.3.3.3.5) (532)
3.3.3.3.6 (632)	3.3.3.3.7 (732)	3.3.3.3.8 (832)

Dual tiling

The dual tiling is called an order-7-3 floret pentagonal tiling, and is related to the floret pentagonal tiling.

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)

See also

• Snub hexagonal tiling
  • Floret pentagonal tiling
• Order-3 heptagonal tiling
• Tilings of regular polygons
• List of uniform planar tilings
• Kagome lattice

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