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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
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

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

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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}
Spherical Euclidean Hyperbolic tilings

{6,2}

{6,3}

{6,4}

{6,5}

{6,6}

{6,7}

{6,8}
...
{6,∞}

See also

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References

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  • 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.
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