The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.

An “aperiodic monotile,” or einstein, is a shape that tiles an infinite flat surface in a nonrepeating pattern. The authors of a new paper called their einstein “the hat,” as it resembles ...

After half a century, mathematicians succeed in finding an ‘einstein,’ a shape that forms a tiled pattern that never repeats.