Order-5 pentagonal tiling

Order-5 pentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration55
Schläfli symbol{5,5}
Wythoff symbol5 | 5 2
Coxeter diagram
Symmetry group[5,5], (*552)
Dualself dual
PropertiesVertex-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

{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 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.
  • Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
  • Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
  • Hyperbolic and Spherical Tiling Gallery
  • KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
  • Hyperbolic Planar Tessellations, Don Hatch
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