Snub triapeirogonal tiling

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Snub triapeirogonal tiling
Snub triapeirogonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.3.3.∞
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}.

Images[edit]

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

H2 snub 23ia.pngH2 snub 23ib.png

The dual tiling:

Order-3-infinite floret pentagonal tiling.png

Related polyhedra and tiling[edit]

This hyperbolic tiling is topologically related as a part of sequence of uniform snub polyhedra with vertex configurations (3.3.3.3.n), and [n,3] Coxeter group symmetry.

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]