Truncated order-6 pentagonal tiling

Truncated order-6 pentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration6.10.10
Schläfli symbolt{5,6}
t(5,5,3)
Wythoff symbol2 6 | 5
3 5 5 |
Coxeter diagram
Symmetry group[6,5], (*652)
[(5,5,3)], (*553)
DualOrder-5 hexakis hexagonal tiling
PropertiesVertex-transitive

In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.

Uniform colorings


t012(5,5,3)
With mirrors
An alternate construction exists from the [(5,5,3)] family, as the omnitruncation t012(5,5,3). It is shown with two (colors) of decagons.

Symmetry

The dual of this tiling represents the fundamental domains of the *553 symmetry. There are no mirror removal subgroups of [(5,5,3)], but this symmetry group can be doubled to 652 symmetry by adding a bisecting mirror to the fundamental domains.

Small index subgroups of [(5,5,3)]
Type Reflective domains Rotational symmetry
Index 1 2
Diagram
Coxeter
(orbifold)		 [(5,5,3)] =
(*553)		 [(5,5,3)]+ =
(553)
[(5,5,3)] reflective symmetry uniform tilings

References

See also

Wikimedia Commons has media related to Uniform tiling 6-10-10.

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