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Contents

   



(Top)
 


1 Uniform colorings  





2 Symmetry  





3 Related polyhedra and tiling  





4 References  





5 See also  





6 External links  














Truncated order-6 pentagonal tiling







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From Wikipedia, the free encyclopedia
 


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
Symmetry group [6,5], (*652)
[(5,5,3)], (*553)
Dual Order-5 hexakis hexagonal tiling
Properties Vertex-transitive

Ingeometry, 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[edit]


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[edit]

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)

Related polyhedra and tiling[edit]

Uniform hexagonal/pentagonal tilings
  • t
  • e
  • Symmetry: [6,5], (*652) [6,5]+, (652) [6,5+], (5*3) [1+,6,5], (*553)
    {6,5} t{6,5} r{6,5} 2t{6,5}=t{5,6} 2r{6,5}={5,6} rr{6,5} tr{6,5} sr{6,5} s{5,6} h{6,5}
    Uniform duals
    V65 V5.12.12 V5.6.5.6 V6.10.10 V56 V4.5.4.6 V4.10.12 V3.3.5.3.6 V3.3.3.5.3.5 V(3.5)5
    [(5,5,3)] reflective symmetry uniform tilings

    References[edit]

    See also[edit]

    External links[edit]


    Retrieved from "https://en.wikipedia.org/w/index.php?title=Truncated_order-6_pentagonal_tiling&oldid=1189589665"

    Categories: 
    Hyperbolic tilings
    Isogonal tilings
    Order-6 tilings
    Pentagonal tilings
    Truncated tilings
    Uniform tilings
    Hidden category: 
    Commons category link is on Wikidata
     



    This page was last edited on 12 December 2023, at 20:12 (UTC).

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