Infinite-order hexagonal tiling

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.

Infinite-order hexagonal tiling
Infinite-order hexagonal tiling
Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration6
Schläfli symbol{6,}
Wythoff symbol | 6 2
Coxeter diagram
Symmetry group[,6], (*62)
DualOrder-6 apeirogonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive

Symmetry

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}
Spherical Euclidean Hyperbolic tilings

{6,2}

{6,3}

{6,4}

{6,5}

{6,6}

{6,7}

{6,8}
...
{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.
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