Snub triapeirogonal tiling


Snub triapeirogonal tiling
Snub triapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration∞
Schläfli symbol sr{∞,3} or
Wythoff symbol | ∞ 3 2
Coxeter diagram CDel node h.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png or CDel node h.pngCDel split1-i3.pngCDel nodes hh.png
Symmetry group [∞,3]+, (∞32)
Dual Order-3-infinite floret pentagonal tiling
Properties Vertex-transitive Chiral

In geometry, the snub triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of sr{∞,3}.


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


The dual tiling:


Related polyhedra and tilingEdit

This hyperbolic tiling is topologically related as a part of sequence of uniform snub polyhedra with vertex configurations (, and [n,3] Coxeter group symmetry.

n32 symmetry mutations of snub tilings:
Spherical Euclidean Compact hyperbolic Paracomp.
232 332 432 532 632 732 832 ∞32
Config.∞ Gyrofigures                
Config. V3. V3. V3. V3. V3. V3. V3. V3.3.3.3.∞
Paracompact uniform tilings in [∞,3] family
Symmetry: [∞,3], (*∞32) [∞,3]+
{∞,3} t{∞,3} r{∞,3} t{3,∞} {3,∞} rr{∞,3} tr{∞,3} sr{∞,3} h{∞,3} h2{∞,3} s{3,∞}
Uniform duals
V∞3 V3.∞.∞ V(3.∞)2 V6.6.∞ V3 V4.3.4.∞ V4.6.∞ V3.3.3.3.∞ V(3.∞)3 V3.∞

See alsoEdit


  • 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 linksEdit