Pentaapeirogonal tiling

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pentaapeirogonal tiling
Pentaapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (5.∞)2
Schläfli symbol r{∞,5} or
Wythoff symbol 2 | ∞ 5
Coxeter diagram CDel node.pngCDel infin.pngCDel node 1.pngCDel 5.pngCDel node.png or CDel node 1.pngCDel split1-i5.pngCDel nodes.png
Symmetry group [∞,5], (*∞52)
Dual
Properties Vertex-transitive edge-transitive

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

Related polyhedra and tiling[]

*5n2 symmetry mutations of quasiregular tilings: (5.n)2
  • v
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 Uniform tiling 532-t1.png H2-5-4-rectified.svg H2 tiling 255-2.png H2 tiling 256-2.png H2 tiling 257-2.png H2 tiling 258-2.png H2 tiling 25i-2.png
Config. (5.3)2 (5.4)2 (5.5)2 (5.6)2 (5.∞)2 (5.ni)2
Rhombic
figures 		Rhombictriacontahedron.jpg H2-5-4-rhombic.svg H2-5-4-primal.svg 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

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.

External links[]

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