Rhombipentahexagonal tiling

Short description: Uniform tiling of the hyperbolic plane in geometry

Rhombipentahexagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	5.4.6.4
Schläfli symbol	rr{6,5} or $r\left\{\begin{array}{c}6\\ 5\end{array}\right\}$
Wythoff symbol	5 | 6 2
Coxeter diagram
Symmetry group	[6,5], (*652)
Dual	Deltoidal pentahexagonal tiling
Properties	Vertex-transitive

In geometry, the rhombipentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_0,2{6,5}.

Related polyhedra and tiling

Uniform hexagonal/pentagonal tilings
Symmetry: [6,5], (*652)							[6,5]+, (652)	[6,5+], (5*3)	[1+,6,5], (*553)
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{6,5}	t{6,5}	r{6,5}	2t{6,5}=t{5,6}	2r{6,5}={5,6}	rr{6,5}	tr{6,5}	sr{6,5}	s{5,6}	h{6,5}
Uniform duals
V65	V5.12.12	V5.6.5.6	V6.10.10	V56	V4.5.4.6	V4.10.12	V3.3.5.3.6	V3.3.3.5.3.5	V(3.5)5

References

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

See also

• Square tiling
• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

External links

• Weisstein, Eric W.. "Hyperbolic tiling". http://mathworld.wolfram.com/HyperbolicTiling.html. 
• Weisstein, Eric W.. "Poincaré hyperbolic disk". http://mathworld.wolfram.com/PoincareHyperbolicDisk.html. 
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch