Hat

The hat is a polygon, which along with it's mirror image can tessellate the plane, but only non-periodically. This makes it a solution to some formulations of the einstein problem. It can be formed as an outer-blend of eight 60&deg;-90&deg;-120&deg;-90&deg; kites, or 4 mirror-symmetric pentagons.

Two of its sides meet at an angle of, making them appear as a single edge. However there must be a vertex at that location for the aperiodic tiling to work.