Floret pentagonal tiling

Floret pentagonal tiling

Infobox face-uniform tiling


Type=Dual semiregular tiling
Face_List=irregular pentagons
Symmetry_Group=p6
or 632
Face_Type=V3.3.3.3.6
Dual=Snub hexagonal tiling
Property_List=face-transitive, chiral

In geometry, the Floret pentagonal tiling is a dual semiregular tiling of the Euclidean plane. It is the dual of the snub hexagonal tiling.

Conway calls it a 6-fold pentille.

It is given its name because its six pentagonal tiles radiate out from a central point, like petals on a flower.

This tiling is topologically related as a part of sequence of polyhedra of pentagons with face configurations (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any "n".) These face-transitive figures have (n32) rotational symmetry.

See also

* Tilings of regular polygons
* List of uniform tilings

References

* (Chapter 2.1: "Regular and uniform tilings", p.58-65)
* Williams, Robert "The Geometrical Foundation of Natural Structure: A Source Book of Design" New York: Dover, 1979. p39

External links

* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, "The Symmetry of Things" 2008, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205]
* [http://www.steelpillow.com/polyhedra/five_sf/five.htm Five space-filling polyhedra] by Guy Inchbald
* [http://demonstrations.wolfram.com/PentagonalTiling/ Pentagonal Tiling] by Sándor Kabai, The Wolfram Demonstrations Project.


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