Snub triapeirogonal tiling

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

Snub triapeirogonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration3.3.3.3.
Schläfli symbolsr{,3} or
Wythoff symbol| 3 2
Coxeter diagram or
Symmetry group[,3]+, (32)
DualOrder-3-infinite floret pentagonal tiling
PropertiesVertex-transitive Chiral

Images

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

The dual tiling:

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.

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See also

References

    • 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.
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