BREAKING NEWS
Order-5 pentagonal tiling

Summary

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.

Related tilings

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)

=

=

=

=

=

=

=

=

{5,5} t{5,5}
r{5,5} 2t{5,5}=t{5,5} 2r{5,5}={5,5} rr{5,5} tr{5,5} sr{5,5}
Uniform duals