An Aperiodic Hexagonal Tile

By Edward Newkirk

April 8, 2013

Abstract

Have you ever felt like most tilings of the plane are a little repetitive? Like once you've seen one part of a tiling, you've seen it all? We'll summarize the history of the search for aperiodic sets of tiles, then introduce a single tile which can cover the plane (with reflection) but never with translational symmetry.