Snub tetrapentagonal tiling

Summary

Snub tetrapentagonal tiling
Snub tetrapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.4.3.5
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}.

ImagesEdit

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 V3.3.4.3.5.

 

Related polyhedra and tilingEdit

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

4n2 symmetry mutations of snub tilings: 3.3.4.3.n
Symmetry
4n2
Spherical Euclidean Compact hyperbolic Paracomp.
242 342 442 542 642 742 842 ∞42
Snub
figures
               
Config. 3.3.4.3.2 3.3.4.3.3 3.3.4.3.4 3.3.4.3.5 3.3.4.3.6 3.3.4.3.7 3.3.4.3.8 3.3.4.3.∞
Gyro
figures
       
Config. V3.3.4.3.2 V3.3.4.3.3 V3.3.4.3.4 V3.3.4.3.5 V3.3.4.3.6 V3.3.4.3.7 V3.3.4.3.8 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 V3.3.4.3.5 V3.3.5.3.5 V55

See alsoEdit

ReferencesEdit

  • 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