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Order-5 pentagonal tiling
Order-5 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 55
Schläfli symbol {5,5}
Wythoff symbol 5 | 5 2
Coxeter diagram CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel node.png
Symmetry group [5,5], (*552)
Dual self dual
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {5,5}, constructed from five pentagons around every vertex. As such, it is self-dual.

Related tilingsEdit

Spherical Hyperbolic tilings
 
{2,5}
     
 
{3,5}
     
 
{4,5}
     
 
{5,5}
     
 
{6,5}
     
 
{7,5}
     
 
{8,5}
     
...  
{∞,5}
     

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).

Finite Compact hyperbolic Paracompact
 
{5,3}
     
 
{5,4}
     
 
{5,5}
     
 
{5,6}
     
 
{5,7}
     
 
{5,8}...
     
 
{5,∞}
     

See alsoEdit

ReferencesEdit

  • 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 linksEdit