Snub pentapentagonal tiling

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Snub pentapentagonal tiling
Snub pentapentagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.3.5.3.5
Schläfli symbol s{5,4}
sr{5,5}
Wythoff symbol | 5 5 2
Coxeter diagram CDel node h.pngCDel 5.pngCDel node h.pngCDel 4.pngCDel node.png
CDel node h.pngCDel 5.pngCDel node h.pngCDel 5.pngCDel node h.png or CDel node h.pngCDel split1-55.pngCDel nodes hh.png
Symmetry group [5+,4], (5*2)
[5,5]+, (552)
Dual Order-5-5 floret pentagonal tiling
Properties Vertex-transitive

In geometry, the snub pentapentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of sr{5,5}, constructed from two regular pentagons and three equilateral triangles around every vertex.

Images[edit]

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

H2 snub 255a.pngH2 snub 255b.png

Symmetry[edit]

A double symmetry coloring can be constructed from [5,4] symmetry with only one color pentagon. It has Schläfli symbol s{5,4}, and Coxeter diagram CDel node h.pngCDel 5.pngCDel node h.pngCDel 4.pngCDel node.png.

Uniform tiling 542-h01.png

Related tilings[edit]

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]