The shape 'chiral', which achieves aperiodic tiling, is shown filling a plane without a repeating pattern. Courtesy of David Smith Amateur mathematicians have discovered a shape that can infinitely ...

A new shape called an einstein has taken the math world by storm. The craggy, hat-shaped tile can cover an infinite plane with patterns that never repeat. Creatively tiling a bathroom floor isn’t just ...

Infinitely many copies of a 13-sided shape can be arranged with no overlaps or gaps in a pattern that never repeats. David Smith, Joseph Samuel Myers, Craig S. Kaplan and Chaim Goodman-Strauss (CC BY ...

Mathematicians have discovered a single shape that can be used to cover a surface completely without ever creating a repeating pattern. The long-sought shape is surprisingly simple but has taken ...

The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way. In mid-November of ...