Tetraapeirogonal tiling
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In geometry, the tetraapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,4}.
Uniform constructions
There are 3 lower symmetry uniform construction, one with two colors of apeirogons, one with two colors of squares, and one with two colors of each:
| Symmetry | (*∞42) [∞,4] |
(*∞33) [1+,∞,4] = [(∞,4,4)] |
(*∞∞2) [∞,4,1+] = [∞,∞] |
(*∞2∞2) [1+,∞,4,1+] |
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| Schläfli | r{∞,4} | r{4,∞}1⁄2 | r{∞,4}1⁄2=rr{∞,∞} | r{∞,4}1⁄4 |
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Symmetry
The dual to this tiling represents the fundamental domains of *∞2∞2 symmetry group. The symmetry can be doubled by adding mirrors on either diagonal of the rhombic domains, creating *∞∞2 and *∞44 symmetry.
Related polyhedra and tiling
See also
- List of uniform planar tilings
- Tilings of regular polygons
- Uniform tilings in hyperbolic plane
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, 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.
External links
- Weisstein, Eric W.. "Hyperbolic tiling". http://mathworld.wolfram.com/HyperbolicTiling.html.
- Weisstein, Eric W.. "Poincaré hyperbolic disk". http://mathworld.wolfram.com/PoincareHyperbolicDisk.html.
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