This Surprisingly Simple Shape Solves a Longstanding Mathematical Problem : ScienceAlert

A group of mathematicians has unveiled a brand new 13-sided shape they’ve simply called ‘the hat’.

Don’t let the rather mundane description fool you though. This hat (which looks a bit like a fedora) is next season’s must-have fashion item, able to be tiled across a plane to create patterns that never repeat.

Shapes like these are known as aperiodic monotiles, or einsteins. Slotted together, it’s impossible to find a matching arrangement or orientation somewhere directly above or on the same horizon.

The hat was first identified by non-professional mathematician and “shape hobbyist” David…