Snub hexaoctagonal tiling

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Snub hexaoctagonal tiling
Snub hexaoctagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.6.3.8
Schläfli symbol sr{8,6} or
Wythoff symbol | 8 6 2
Coxeter diagram CDel node h.pngCDel 8.pngCDel node h.pngCDel 6.pngCDel node h.png or CDel node h.pngCDel split1-86.pngCDel nodes hh.png
Symmetry group [8,6]+, (862)
Dual Order-8-6 floret pentagonal tiling
Properties Vertex-transitive Chiral

In geometry, the snub hexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. There are three triangles, one hexagon, and one octagon on each vertex. It has Schläfli symbol of sr{8,6}.

Images[edit]

Drawn in chiral pairs, with edges missing between black triangles:

H2 snub 268a.pngH2 snub 268b.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]