Snub tetrapentagonal tiling

In geometry, the snub tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,4}.

Snub tetrapentagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration3.3.4.3.5
Schläfli symbolsr{5,4} or
Wythoff symbol| 5 4 2
Coxeter diagram or
Symmetry group[5,4]+, (542)
DualOrder-5-4 floret pentagonal tiling
PropertiesVertex-transitive Chiral

Images

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

Dual tiling

The dual is called an order-5-4 floret pentagonal tiling, defined by face configuration V3.3.4.3.5.

The snub tetrapentagonal tiling is fourth in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.

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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