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Mathematical Object

Penrose Tiling

Geometry

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.

Facts
Classification
Object Kind
Geometric Object 1
Origin Year
1974 1
Connections

Attributed To

Source Penrose Tiling (Wikipedia)

Is Kind Of Object

Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.

Sources
1. Penrose Tiling (Wikipedia)
  • 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
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