Snub pentahexagonal tiling

Snub pentahexagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.5.3.6
Schläfli symbol	sr{6,5} or $s{\begin{Bmatrix}6\\5\end{Bmatrix}}$
Wythoff symbol	| 6 5 2
Coxeter diagram
Symmetry group	[6,5]+, (652)
Dual	Order-6-5 floret pentagonal tiling
Properties	Vertex-transitive Chiral

In geometry, the snub pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{6,5}.

Images

Drawn in chiral pairs, with edges missing between black triangles:

Related polyhedra and tiling

Uniform hexagonal/pentagonal tilings
Symmetry: [6,5], (*652)							[6,5]+, (652)	[6,5+], (5*3)	[1+,6,5], (*553)
{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. LCCN 99035678.

See also

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

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch