Infinite-order hexagonal tiling

Infinite-order hexagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic regular tiling
Vertex configuration	6∞
Schläfli symbol	{6,∞}
Wythoff symbol	∞ | 6 2
Coxeter diagram
Symmetry group	[∞,6], (*∞62)
Dual	Order-6 apeirogonal tiling
Properties	Vertex-transitive, edge-transitive, face-transitive

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.

There is a half symmetry form, , seen with alternating colors:

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

*n62 symmetry mutation of regular tilings: {6,n} v t e
Spherical	Euclidean	Hyperbolic tilings
{6,2}	{6,3}	{6,4}	{6,5}	{6,6}	{6,7}	{6,8}	...	{6,∞}

Wikimedia Commons has media related to Infinite-order hexagonal tiling.

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

• 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. LCCN 99035678.

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24 at the Wayback Machine