Order-5 pentagonal tiling

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Short description: Regular tiling of the hyperbolic plane


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
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.

Spherical Hyperbolic tilings [v · d · e]

{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). Template:Regular pentagonal tiling table

See also

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, 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. 




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