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词条 Snub pentapentagonal tiling
释义

  1. Images

  2. Symmetry

  3. Related tilings

  4. See also

  5. References

  6. External links

{{Uniform hyperbolic tiles db|Uniform hyperbolic tiling stat table|U55_s}}

In geometry, the snub pentapentagonal tiling is a uniform 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

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

Symmetry

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 {{CDD|node_h|5|node_h|4|node}}.

Related tilings

{{Order_5-5_tiling_table}}{{Order_5-4_tiling_table}}{{Snub5 table}}

See also

{{Commonscat|Uniform tiling 3-3-5-3-5}}
  • Square tiling
  • Uniform tilings in hyperbolic plane
  • List of regular polytopes

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)
  • {{Cite book|title=The Beauty of Geometry: Twelve Essays|year=1999|publisher=Dover Publications|lccn=99035678|isbn=0-486-40919-8|chapter=Chapter 10: Regular honeycombs in hyperbolic space}}

External links

  • {{MathWorld | urlname= HyperbolicTiling | title = Hyperbolic tiling}}
  • {{MathWorld | urlname=PoincareHyperbolicDisk | title = Poincaré hyperbolic disk }}
  • Hyperbolic and Spherical Tiling Gallery
  • KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
  • Hyperbolic Planar Tessellations, Don Hatch
{{Tessellation}}

3 : Hyperbolic tilings|Isogonal tilings|Snub tilings

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