tetrapentagonal tiling
{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U54_1}}
In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1{4,5} or r{4,5}.
Symmetry
A half symmetry [1+,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.
Dual tiling
The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:
Related polyhedra and tiling
{{Order 5-4 tiling table}}
{{Order 5-5 tiling table}}
{{Quasiregular4 table}}
{{Quasiregular5 table}}
See also
{{Commonscat|Uniform tiling 4-5-4-5}}
- Binary tiling, an aperiodic tiling of the hyperbolic plane by pentagons
- Uniform tilings in hyperbolic plane
- List of regular polytopes
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}}
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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