Aperiodic tiling, in which shapes can fit together to create infinite patterns that never repeat, has fascinated mathematicians for decades, but until now no one knew if it could be done with just one shape

By Matthew Sparkes

Aperiodic tiling

This single shape produces a pattern that never repeats

David Smith, Joseph Myers, Chaim Goodman-Strauss and Craig S. Kaplan

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken decades to uncover – and could find uses in everything from material science to decorating.

Simple shapes such as squares and equilateral triangles can tile, or snugly cover a surface without gaps, in a repeating pattern that will be familiar to anyone who has stared at a bathroom wall. Mathematicians are interested in …

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