Order-5 hexagonal tiling

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Order-5 hexagonal tiling
Order-5 hexagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 65
Schläfli symbol {6,5}
Wythoff symbol 5 | 6 2
Coxeter diagram CDel node 1.pngCDel 6.pngCDel node.pngCDel 5.pngCDel node.png
Symmetry group [6,5], (*652)
Dual Order-6 pentagonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

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

Related polyhedra and tiling[edit]

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 CDel node 1.pngCDel n.pngCDel node.pngCDel 5.pngCDel node.png, progressing to infinity.

Spherical Hyperbolic tilings
Spherical pentagonal hosohedron.png
{2,5}
CDel node 1.pngCDel 2.pngCDel node.pngCDel 5.pngCDel node.png
Uniform tiling 532-t2.png
{3,5}
CDel node 1.pngCDel 3.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 245-1.png
{4,5}
CDel node 1.pngCDel 4.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 255-1.png
{5,5}
CDel node 1.pngCDel 5.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 256-1.png
{6,5}
CDel node 1.pngCDel 6.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 257-1.png
{7,5}
CDel node 1.pngCDel 7.pngCDel node.pngCDel 5.pngCDel node.png
H2 tiling 258-1.png
{8,5}
CDel node 1.pngCDel 8.pngCDel node.pngCDel 5.pngCDel node.png
... H2 tiling 25i-1.png
{∞,5}
CDel node 1.pngCDel infin.pngCDel node.pngCDel 5.pngCDel node.png

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 CDel node 1.pngCDel 6.pngCDel node.pngCDel n.pngCDel node.png, progressing to infinity.

References[edit]

  • 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[edit]

External links[edit]