Order-5 hexagonal tiling

In geometry, the order-5 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {6,5}.

Order-5 hexagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration65
Schläfli symbol{6,5}
Wythoff symbol6 2
Coxeter diagram
Symmetry group[6,5], (*652)
DualOrder-6 pentagonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive

This tiling is topologically related as a part of sequence of regular tilings with order-5 vertices with Schläfli symbol {n,5}, and Coxeter diagram , progressing to infinity.

Spherical Hyperbolic tilings

{2,5}

{3,5}

{4,5}

{5,5}

{6,5}

{7,5}

{8,5}
...
{,5}

This tiling is topologically related as a part of sequence of regular tilings with hexagonal faces, starting with the hexagonal tiling, with Schläfli symbol {6,n}, and Coxeter diagram , progressing to infinity.

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

See also

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