Pentahexagonal tiling

Pentahexagonal tiling
Pentahexagonal tiling Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	(5.62
Schläfli symbol	r{6,5} or $\left\{\begin{array}{c}6\\ 5\end{array}\right\}$
Wythoff symbol	2 | 6 5
Coxeter diagram	Template:CDD
Symmetry group	[6,5], (*652)
Dual	Order-6-5 rhombille tiling
Properties	Vertex-transitive edge-transitive

In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t₁{6,5}.

Uniform colorings

File:H2 tiling 355-5.png

Related polyhedra and tiling

*5n2 symmetry mutations of quasiregular tilings: (5.n)2
Symmetry *5n2 [n,5]	Spherical	Hyperbolic					Paracompact	Noncompact
	*352 [3,5]	*452 [4,5]	*552 [5,5]	*652 [6,5]	*752 [7,5]	*852 [8,5]...	*∞52 [∞,5]	[ni,5]
Figures	File:Uniform tiling 532-t1.png	File:H2-5-4-rectified.svg	File:H2 tiling 255-2.png	File:H2 tiling 256-2.png	File:H2 tiling 257-2.png	File:H2 tiling 258-2.png	File:H2 tiling 25i-2.png
Config.	(5.3)2	(5.4)2	(5.5)2	(5.6)2	(5.7)2	(5.8)2	(5.∞)2	(5.ni)2
Rhombic figures	File:Rhombictriacontahedron.svg	File:H2-5-4-rhombic.svg	File:H2-5-4-primal.svg	File:Order-6-5 quasiregular rhombic tiling.png
Config.	V(5.3)2	V(5.4)2	V(5.5)2	V(5.6)2	V(5.7)2	V(5.8)2	V(5.∞)2	V(5.∞)2

Symmetry mutation of quasiregular tilings: (6.n)2
Symmetry *6n2 [n,6]	Euclidean	Compact hyperbolic					Paracompact	Noncompact
	*632 [3,6]	*642 [4,6]	*652 [5,6]	*662 [6,6]	*762 [7,6]	*862 [8,6]...	*∞62 [∞,6]	[iπ/λ,6]
Quasiregular figures configuration	File:Uniform tiling 63-t1.svg 6.3.6.3	File:H2 tiling 246-2.png 6.4.6.4	File:H2 tiling 256-2.png 6.5.6.5	File:H2 tiling 266-2.png 6.6.6.6	File:H2 tiling 267-2.png 6.7.6.7	File:H2 tiling 268-2.png 6.8.6.8	File:H2 tiling 26i-2.png 6.∞.6.∞	6.∞.6.∞
Dual figures
Rhombic figures configuration	File:Rhombic star tiling.svg V6.3.6.3	File:H2chess 246a.png V6.4.6.4	File:Order-6-5 quasiregular rhombic tiling.png V6.5.6.5	File:H2 tiling 246-4.png V6.6.6.6	V6.7.6.7	File:H2chess 268a.png V6.8.6.8	File:H2chess 26ia.png V6.∞.6.∞

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, Template:Isbn (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

• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch