Infinite-order pentagonal tiling
{{Uniform hyperbolic tiles db|Reg hyperbolic tiling stat table|Ui5_2}}
In 2-dimensional hyperbolic geometry, the infinite-order pentagonal tiling is a regular tiling. It has Schläfli symbol of {5,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
Symmetry
There is a half symmetry form, {{CDD|node_1|split1-55|branch|labelinfin}}, seen with alternating colors:
Related polyhedra and tiling
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).
{{Regular pentagonal tiling table}}
{{Order i-5 tiling table}}
See also
{{Commons category|Infinite-order pentagonal tiling}}
References
{{Reflist}}
- {{Cite book|title=The Symmetries of Things|year=2008|isbn=978-1-56881-220-5|chapter=Chapter 19, The Hyperbolic Archimedean Tessellations|author1=John H. Conway|author-link=John Horton Conway|author2=Heidi Burgiel|author3=Chaim Goodman-Strauss|publisher=Taylor & Francis }}
- {{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|author=H. S. M. Coxeter|author-link=Harold Scott MacDonald Coxeter}}
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] {{Webarchive|url=https://web.archive.org/web/20130324095520/http://bork.hampshire.edu/~bernie/hyper/ |date=2013-03-24 }}
{{Tessellation}}