A Penrose tiling is a way of covering a plane completely with non-overlapping polygons that never repeats in a regular, periodic pattern no matter how far it extends. The mathematician and physicist Roger Penrose introduced the first such tiling in a 1974 paper, later simplifying it to versions built from just two prototile shapes, either two rhombi or a pair called kites and darts. Despite having no translational symmetry, a Penrose tiling can show reflection symmetry and fivefold rotational symmetry, and its patterns are self-similar across scales. The tilings turned out to describe real physical quasicrystals, materials whose atoms are arranged in an ordered but non-repeating structure, a discovery that earned Dan Shechtman the 2011 Nobel Prize in Chemistry.
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Penrose Tiling
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Section: Development of the Penrose tilings
The first Penrose tiling (tiling P1 below) is an aperiodic set of six prototiles, introduced by Roger Penrose in a 1974 paper
Attributed To: Roger Penrose, Lead paragraph
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by non-overlapping polygons or other
In Branch: Geometry, Lead section
A Penrose tiling is an example of an aperiodic tiling. Here, a tiling is a covering of the plane by
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In 1974, Penrose discovered Penrose tilings, which are formed from two tiles that can only tile the plane nonperiodically, and are the first tilings to exhibit fivefold rotational symmetry.
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