Mathematicians have finally discovered an elusive ‘einstein’ tile

A 13-sided shape known as “the hat” has mathematicians tipping their caps.

It’s the first true example of an “einstein,” a single shape that forms a special tiling of a plane: Like bathroom floor tile, it can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats.

“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…