1. Symmetry

2. Related polyhedra and tiling

3. See also

4. References

5. External links

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, {{CDD|node_1|split1-66|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 (6ⁿ).

See also

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

References

• {{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|author2=Heidi Burgiel|author3=Chaim Goodman-Strass}}
• {{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}}

External links

• {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
• {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
• Hyperbolic and Spherical Tiling Gallery

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