Pentaapeirogonal tiling

In geometry, the pentaapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,5}.

pentaapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	(5.∞)^2
Schläfli symbol	r{∞,5} or ${\displaystyle {\begin{Bmatrix}\infty \\5\end{Bmatrix}}}$
Wythoff symbol	∞ 5
Coxeter diagram	or
Symmetry group	[∞,5], (*∞52)
Dual	Order-5-infinite rhombille tiling
Properties	Vertex-transitive edge-transitive

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
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
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

See also

• List of uniform planar tilings
• Tilings of regular polygons
• Uniform tilings in hyperbolic plane

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)
• "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

External links

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.