A 13-sided tile called “the hat” forms a pattern that covers an infinite plane yet it cannot repeat, making it a long-sought shape known as an “einstein”.
“Everybody is astonished and is delighted, both,” says mathematician Marjorie Senechal of Smith College in Northampton, Mass., who was not involved with the discovery. Mathematicians had been searching for such a shape for half a century. “It wasn’t even clear that such a thing could exist,” Senechal says.