Mathematicians create 'impossible' Einstein tile for perfect tiling without repetition.

Mathematicians have discovered a new 13-sided shape called "The hat" that can completely cover a surface without ever creating a repeated pattern, making it an aperiodic tile. The shape was discovered by an amateur mathematician and a professor at the University of Waterloo in Canada. The finding has created quite a stir since its release in late March and could be significant across other fields of research, according to experts. The shape is publicly available and not going to be copyrighted.