Truncated order-4 pentagonal tiling

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Truncated pentagonal tiling
Truncated order-4 pentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 4.10.10
Schläfli symbol t{5,4}
Wythoff symbol 2 4 | 5
2 5 5 |
Coxeter diagram CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 4.pngCDel node.png
CDel node 1.pngCDel 5.pngCDel node 1.pngCDel 5.pngCDel node 1.png or CDel node 1.pngCDel split1-55.pngCDel nodes 11.png
Symmetry group [5,4], (*542)
[5,5], (*552)
Dual Order-5 tetrakis square tiling
Properties Vertex-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[edit]

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.

Uniform tiling 552-t012.png

Symmetry[edit]

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 552 symmetry 000.png 552 symmetry aaa.png
Coxeter
(orbifold)
[5,5] = CDel node c1.pngCDel 5.pngCDel node c1.pngCDel 5.pngCDel node c1.png = CDel node c1.pngCDel split1-55.pngCDel branch c1.pngCDel label2.png
(*552)
[5,5]+ = CDel node h2.pngCDel 5.pngCDel node h2.pngCDel 5.pngCDel node h2.png = CDel node h2.pngCDel split1-55.pngCDel branch h2h2.pngCDel label2.png
(552)

Related polyhedra and tiling[edit]

References[edit]

  • 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)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

See also[edit]

External links[edit]