Snub triapeirotrigonal tiling

Summary

Snub triapeirotrigonal tiling
Snub triapeirotrigonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.3.3.3.∞
Schläfli symbol s{3,∞}
s(∞,3,3)
Wythoff symbol | ∞ 3 3
Coxeter diagram
Symmetry group [(∞,3,3)]+, (∞33)
Dual Order-i-3-3_t0 dual tiling
Properties Vertex-transitive Chiral

In geometry, the snub triapeirotrigonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of s{3,∞}.

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Paracompact hyperbolic uniform tilings in [(∞,3,3)] family
Symmetry: [(∞,3,3)], (*∞33) [(∞,3,3)]+, (∞33)
                                       
                                               
               
(∞,∞,3) t0,1(∞,3,3) t1(∞,3,3) t1,2(∞,3,3) t2(∞,3,3) t0,2(∞,3,3) t0,1,2(∞,3,3) s(∞,3,3) Dual tilings                                                                                                                    
V(3.∞)3 V3.∞.3.∞ V(3.∞)3 V3.6.∞.6 V(3.3) V3.6.∞.6 V6.6.∞ V3.3.3.3.3.∞

References

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  • 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)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

See also

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  • Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
  • Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
  • Hyperbolic and Spherical Tiling Gallery
  • KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
  • Hyperbolic Planar Tessellations, Don Hatch