Rhombihexaoctagonal tiling

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Rhombihexaoctagonal tiling
Rhombihexaoctagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 6.4.8.4
Schläfli symbol rr{8,6} or
Wythoff symbol 6 | 8 2
Coxeter diagram CDel node 1.pngCDel 8.pngCDel node.pngCDel 6.pngCDel node 1.png
Symmetry group [8,6], (*862)
Dual Deltoidal hexaoctagonal tiling
Properties Vertex-transitive

In geometry, the rhombihexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. It has Schläfli symbol of rr{8,6}.

Symmetry[edit]

The dual tiling, called a deltoidal hexaoctagonal tiling represent the fundamental domains of *4232 symmetry, a half symmetry of [8,6], (*862) as [8,1+,6].

862 symmetry 0a0.png

Related polyhedra and tilings[edit]

From a Wythoff construction there are fourteen hyperbolic uniform tilings that can be based from the regular order-6 octagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 7 forms with full [8,6] symmetry, and 7 with subsymmetry.

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]