Truncated order-4 pentagonal tiling

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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.

Uniform tiling 552-t012.png

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 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

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, 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. 

See also

External links