Infinite-order hexagonal tiling

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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 CDel node.pngCDel infin.pngCDel node.pngCDel 6.pngCDel node 1.png
CDel node 1.pngCDel split1-66.pngCDel branch.pngCDel labelinfin.png
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.

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).

*n62 symmetry mutation of regular tilings: {6,n}
  • v
Spherical Euclidean Hyperbolic tilings
Hexagonal dihedron.svg
{6,2} 		Uniform tiling 63-t0.svg
{6,3} 		H2 tiling 246-1.png
{6,4} 		H2 tiling 256-1.png
{6,5} 		H2 tiling 266-4.png
{6,6} 		H2 tiling 267-4.png
 H2 tiling 268-4.png
{6,8} 		... H2 tiling 26i-4.png
{6,∞}

See also[]

References[]

  • John H. Conway; Heidi Burgiel; Chaim Goodman-Strass (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.

External links[]

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