Snub hexaoctagonal tiling

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Snub hexaoctagonal tiling
Snub hexaoctagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration
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}.


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]


  • 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]