Truncated order-6 pentagonal tiling

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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

H2 tiling 355-7.png
t012(5,5,3) 		H2 tiling 355-7-mirrors.png
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 553 symmetry 000.png 553 symmetry aaa.png
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 H2 tiling 355-3.png H2 tiling 355-4.png H2 tiling 355-5.png H2 tiling 355-6.png H2 tiling 355-7.png

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

  • Square tiling
  • Tilings of regular polygons
  • List of uniform planar tilings
  • List of regular polytopes

External links



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