Truncated order-6 pentagonal tiling

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Truncated order-6 pentagonal tiling
Truncated order-6 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 6.10.10
Schläfli symbol t{5,6}
t{(5,5,3)}
Wythoff symbol 2 6 | 5
3 5 5 |
Coxeter diagram CDel node.pngCDel 6.pngCDel node 1.pngCDel 5.pngCDel node 1.png
CDel branch 11.pngCDel split2-55.pngCDel node 1.png
Symmetry group [6,5], (*652)
[(5,5,3)], (*553)
Dual Order-5 hexakis hexagonal tiling
Properties Vertex-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

240px
t012(5,5,3)		 240px
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 160px 160px
Coxeter
(orbifold)		 [(5,5,3)] = CDel node c1.pngCDel split1-55.pngCDel branch c1.png
(*553)		 [(5,5,3)]+ = CDel node h2.pngCDel split1-55.pngCDel branch h2h2.png
(553)

Related polyhedra and tiling

[(5,5,3)] reflective symmetry uniform tilings
H2 tiling 355-1.png H2 tiling 355-2.png 60px 60px 60px 60px 60px

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)
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See also

External links

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