Truncated order-4 pentagonal tiling
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U54_01}}
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.
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.
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|+ Small index subgroups of [5,5] |
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!Type !Reflective domains !Rotational symmetry |
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!1 !2 |
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!Diagram |
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|[5,5] = {{CDD|node_c1|5|node_c1|5|node_c1}} = {{CDD|node_c1|split1-55|branch_c1|label2}} |[5,5]+ = {{CDD|node_h2|5|node_h2|5|node_h2}} = {{CDD|node_h2|split1-55|branch_h2h2|label2}} |
Related polyhedra and tiling
{{Truncated_figure3_table}}
{{Order 5-4 tiling table}}
{{Order 5-5 tiling table}}
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 4-10-10}}
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]
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