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Science

Submission + - First Aperiodic Tiling With A Single Shape (technologyreview.com)

KentuckyFC writes: The einstein problem (from ein meaning one and stein meaning tile) is to find a single tile that can cover a 2D plane in a nonrepeating pattern. An answer has eluded some of the world's greatest mathematicians. In 1962, the first nonrepeating tiling was discovered but it required 20,426 shapes. This was later reduced by Roger Penrose who found a way to do it with two shapes: a kite and a dart. Now a pair of mathematicians have discovered the first aperiodic tiling using a single shape. Their solution is a modified hexagon with a 3D shape that determines how the tiles slot together.
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First Aperiodic Tiling With A Single Shape

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