New Shape Discovered Solves Longstanding Math Problem

After a decade of attempts, David Smith, a shape hobbyist, has discovered an "einstein," an aperiodic monotile that tiles a plane in a nonrepeating pattern. Smith's einstein, called "the hat," is a polykite made of eight kites. The paper, co-authored by Smith and three others, provides two proofs of the hat's aperiodicity, one of which uses a new technique. The hat's discovery opens up new possibilities for materials with this type of internal structure.