Order-8 octagonal tiling

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Order-8 octagonal tiling
Order-8 octagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 88
Schläfli symbol {8,8}
Wythoff symbol 8 | 8 2
Coxeter diagram CDel node 1.pngCDel 8.pngCDel node.pngCDel 8.pngCDel node.png
Symmetry group [8,8], (*882)
Dual self dual
Properties Vertex-transitive, edge-transitive, face-transitive

In geometry, the order-8 octagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {8,8} and is self-dual.

Symmetry[edit]

This tiling represents a hyperbolic kaleidoscope of 8 mirrors meeting at a point and bounding regular octagon fundamental domains. This symmetry by orbifold notation is called *44444444 with 8 order-4 mirror intersections. In Coxeter notation can be represented as [8,8*], removing two of three mirrors (passing through the octagon center) in the [8,8] symmetry.

Related polyhedra and tiling[edit]

This tiling is topologically related as a part of sequence of regular tilings with octagonal faces, starting with the octagonal tiling, with Schläfli symbol {8,n}, and Coxeter diagram CDel node 1.pngCDel 8.pngCDel node.pngCDel n.pngCDel node.png, progressing to infinity.

n82 symmetry mutations of regular tilings: 8n
Space Spherical Compact hyperbolic Paracompact
Tiling H2 tiling 238-1.png H2 tiling 248-1.png H2 tiling 258-1.png H2 tiling 268-1.png H2 tiling 278-1.png H2 tiling 288-4.png H2 tiling 28i-4.png
Config. 8.8 83 84 85 86 87 88 ...8

See also[edit]

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. 

External links[edit]