Mathematicians have finally discovered an elusive ‘einstein’ tile

Researchers have discovered the first example of a single shape that can cover a surface with an infinite pattern that never repeats. The shape is surprisingly simple: a 13-sided polykite that the team has dubbed ‘the hat’. The hat’s sides can vary in length without it losing the ability to create ‘aperiodic tiling’. Previous examples of aperiodic tilings, such as Penrose tiles, required two or more shapes.