Infinite-Order Hexagonal Tiling

From Handwiki

In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.

Symmetry

There is a half symmetry form, CDel node 1.pngCDel split1-66.pngCDel branch.pngCDel labelinfin.png, seen with alternating colors:

H2 tiling 66i-4.png

Related polyhedra and tiling

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (6n).

See also

  • Hexagonal tiling
  • Uniform tilings in hyperbolic plane
  • List of regular polytopes

References

  • John H. Conway; Heidi Burgiel; Chaim Goodman-Strauss (2008). "Chapter 19, The Hyperbolic Archimedean Tessellations". The Symmetries of Things. ISBN 978-1-56881-220-5. 
  • H. S. M. Coxeter (1999). "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 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. 
  • Hyperbolic and Spherical Tiling Gallery



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Categories: [Hyperbolic tilings] [Infinite-order tilings] [Isogonal tilings] [Isohedral tilings] [Hexagonal tilings] [Regular tilings]

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