Key Points
It is the first einstein tile to have been found: a shape that can cover a plane without overlapping, leaving gaps, or repeating patterns..
While several ways that tiling exists in nature and the real world (think bathroom tiles or the hexagons of honeycomb), these are periodic and have a translation symmetrythe size, shape and angle remains the same, only the location changes. The 13-sided hat is also a shape that tiles plane, however, it does not possess translational symmetry..
The discovery of the hat shape is the first time a single aperiodic tile has been found to cover a plane..
There are a limited number of aperiodic tiles that have been found over the years since the first tile sets, consisting of 20,000 shapes, were created in 1960s..
Over the years, the number of shapes in a tile has decreased, with British Mathematician Roger Penrose using only two shapes to create an aperiodic tile in the 1970s..
