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truncated order-6 pentagonal tiling

{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U65_12}}

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

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t012(5,5,3)

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With mirrors

colspan=2|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.

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|+ Small index subgroups of [(5,5,3)]

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!Type

!Reflective domains

!Rotational symmetry

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!Index

!1

!2

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!Diagram

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!Coxeter
(orbifold)

|[(5,5,3)] = {{CDD|node_c1|split1-55|branch_c1}}
(*553)

|[(5,5,3)]+ = {{CDD|node_h2|split1-55|branch_h2h2}}
(553)

Related polyhedra and tiling

{{Order 6-5 tiling table}}

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|+ [(5,5,3)] reflective symmetry uniform tilings

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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)
  • {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}

See also

{{Commonscat|Uniform tiling 6-10-10}}

External links

  • {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
  • {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
  • [http://bork.hampshire.edu/~bernie/hyper/ Hyperbolic and Spherical Tiling Gallery]
  • [http://geometrygames.org/KaleidoTile/index.html KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings]
  • [http://www.plunk.org/~hatch/HyperbolicTesselations Hyperbolic Planar Tessellations, Don Hatch]

{{Tessellation}}

Category:Hyperbolic tilings

Category:Isogonal tilings

Category:Order-6 tilings

Category:Pentagonal tilings

Category:Truncated tilings

Category:Uniform tilings