Truncated order-4 pentagonal tiling

Truncated pentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration4.10.10
Schläfli symbolt{5,4}
Wythoff symbol2 4 | 5
2 5 5 |
Coxeter diagram
or
Symmetry group[5,4], (*542)
[5,5], (*552)
DualOrder-5 tetrakis square tiling
PropertiesVertex-transitive

In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.

Uniform colorings

A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling.

Symmetry

There is only one subgroup of [5,5], [5,5]+, removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror.

Small index subgroups of [5,5]
Type Reflective domains Rotational symmetry
Index 1 2
Diagram
Coxeter
(orbifold)		 [5,5] = =
(*552)		 [5,5]+ = =
(552)

References

See also

Wikimedia Commons has media related to Uniform tiling 4-10-10.

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