Floret pentagonal tiling
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| Floret pentagonal tiling | |
|---|---|
 |
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| Type | Dual semiregular tiling |
| Faces | irregular pentagons |
| Face configuration | V3.3.3.3.6 |
| Symmetry group | 632 |
| Dual | Snub hexagonal tiling |
| Properties | face-transitive, chiral |
In geometry, the floret pentagonal tiling is a dual semiregular tiling of the Euclidean plane. It is one of 14 known isohedral pentagon tilings. It is given its name because its six pentagonal tiles radiate out from a central point, like petals on a flower.[1] Conway calls it a 6-fold pentille.[2]
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[edit] Dual tiling
It is the dual of the uniform tiling, snub hexagonal tiling,[3] and has rotational symmetry of orders 6-3-2 symmetry.
[edit] Related polyhedra and tilings
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.
 V3.3.3.3.3 (332) and (532) |
 V3.3.3.3.4 (432) |
 V3.3.3.3.5 (532) |
V3.3.3.3.6 (632) |
 V3.3.3.3.7 (732) |
[edit] See also
[edit] References
- Grünbaum, Branko ; and Shephard, G. C. (1987). Tilings and Patterns. New York: W. H. Freeman. ISBN 0-716-71193-1. (Chapter 2.1: Regular and uniform tilings, p.58-65)
- Williams, Robert (1979). The Geometrical Foundation of Natural Structure: A Source Book of Design. Dover Publications, Inc. ISBN 0-486-23729-X. p.39
[edit] Notes
- ^ Five space-filling polyhedra by Guy Inchbald
- ^ John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 [1] (Chapter 21, Naming Archimedean and Catalan polyhedra and tilings, p288 table)
- ^ Weisstein, Eric W., "Dual tessellation" from MathWorld.
[edit] External links
- Wolfram alpha floret pentagonal tiling
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