Snub tetrapentagonal tiling


Snub tetrapentagonal tiling
Snub tetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration
Schläfli symbol sr{5,4} or
Wythoff symbol | 5 4 2
Coxeter diagram CDel node h.pngCDel 5.pngCDel node h.pngCDel 4.pngCDel node h.png or CDel node h.pngCDel split1-54.pngCDel nodes hh.png
Symmetry group [5,4]+, (542)
Dual Order-5-4 floret pentagonal tiling
Properties Vertex-transitive Chiral

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


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


Dual tilingEdit

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


Related polyhedra and tilingEdit

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

4n2 symmetry mutations of snub tilings:
Spherical Euclidean Compact hyperbolic Paracomp.
242 342 442 542 642 742 842 ∞42
Config. V3. V3. V3. V3. V3. V3. V3. V3.3.4.3.∞
Uniform pentagonal/square tilings
Symmetry: [5,4], (*542) [5,4]+, (542) [5+,4], (5*2) [5,4,1+], (*552)
{5,4} t{5,4} r{5,4} 2t{5,4}=t{4,5} 2r{5,4}={4,5} rr{5,4} tr{5,4} sr{5,4} s{5,4} h{4,5}
Uniform duals
V54 V4.10.10 V4.5.4.5 V5.8.8 V45 V4.4.5.4 V4.8.10 V3. V3. V55

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

  • 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