Snub trioctagonal tiling


Snub trioctagonal tiling
Snub trioctagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration
Schläfli symbol sr{8,3} or
Wythoff symbol | 8 3 2
Coxeter diagram CDel node h.pngCDel 8.pngCDel node h.pngCDel 3.pngCDel node h.png or CDel node h.pngCDel split1-83.pngCDel nodes hh.png or CDel node h.pngCDel split1-83.pngCDel nodes hh.png
Symmetry group [8,3]+, (832)
Dual Order-8-3 floret pentagonal tiling
Properties Vertex-transitive Chiral

In geometry, the order-3 snub octagonal tiling is a semiregular tiling of the hyperbolic plane. There are four triangles, one octagon on each vertex. It has Schläfli symbol of sr{8,3}.


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


Related polyhedra and tilingsEdit

This semiregular tiling is a member of a sequence of snubbed polyhedra and tilings with vertex figure ( and Coxeter–Dynkin diagram      . These figures and their duals have (n32) rotational symmetry, being in the Euclidean plane for n=6, and hyperbolic plane for any higher n. The series can be considered to begin with n=2, with one set of faces degenerated into digons.

n32 symmetry mutations of snub tilings:
Spherical Euclidean Compact hyperbolic Paracomp.
232 332 432 532 632 732 832 ∞32
Config. V3. V3. V3. V3. V3. V3. V3. V3.3.3.3.∞

From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular 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 10 forms.

Uniform octagonal/triangular tilings
Symmetry: [8,3], (*832) [8,3]+
{8,3} t{8,3} r{8,3} t{3,8} {3,8} rr{8,3}
tr{8,3} sr{8,3} h{8,3} h2{8,3} s{3,8}
Uniform duals
V83 V3.16.16 V3.8.3.8 V6.6.8 V38 V3.4.8.4 V4.6.16 V34.8 V(3.4)3 V8.6.6 V35.4


  • 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 alsoEdit

External linksEdit

  • Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
  • Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
  • Hyperbolic and Spherical Tiling Gallery
  • KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
  • Hyperbolic Planar Tessellations, Don Hatch