• A 13-sided tile called 'the hat' forms a pattern that covers an infinite plane yet it cannot repeat
  • This long-sought shape is the first true example of an 'einstein'

Key terms:

  • Einstein: a single shape that forms a special tiling of a plane that can cover an entire surface with no gaps or overlaps but only with a pattern that never repeats
  • The hat: a 13-sided shape that is the first true example of an einstein
  • Aperiodic: a pattern that cannot form a pattern that repeats
  • Polykite: a shape made up of smaller kite shapes stuck together
  • Taylor-Socolar tiles: aperiodic tiles made of multiple disconnected pieces


Research Einstein The Hat Aperiodic Polykite Taylor-Socolar tiles Tiling Patterns Shapes Plane