Order-5 pentagonal tiling

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

{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,∞}
Uniform pentapentagonal tilings
Symmetry: [5,5], (*552) [5,5]+, (552)

=
=
=
=
=
=
=
=
Order-5 pentagonal tiling
{5,5} 		Truncated order-5 pentagonal tiling
t{5,5} 		Order-4 pentagonal tiling
r{5,5} 		Truncated order-5 pentagonal tiling
2t{5,5} = t{5,5} 		Order-5 pentagonal tiling
2r{5,5} = {5,5} 		Tetrapentagonal tiling
rr{5,5} 		Truncated order-4 pentagonal tiling
tr{5,5} 		Snub pentapentagonal tiling
sr{5,5}
Uniform duals
Order-5 pentagonal tiling
V5.5.5.5.5 		V5.10.10 Order-5 square tiling
V5.5.5.5 		V5.10.10 Order-5 pentagonal tiling
V5.5.5.5.5 		V4.5.4.5 V4.10.10 V3.3.5.3.5

See also

Wikimedia Commons has media related to Order-5 pentagonal tiling.

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. LCCN 99035678.


Stub icon

This hyperbolic geometry-related article is a stub. You can help Wikipedia by expanding it.