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
TypeHyperbolic uniform tiling
Vertex configuration(5.∞)2
Schläfli symbolr{∞,5} or
Wythoff symbol2 | ∞ 5
Coxeter diagram or
Symmetry group[∞,5], (*∞52)
DualOrder-5-infinite rhombille tiling
PropertiesVertex-transitive edge-transitive
*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

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.
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