Solved: A single tile that tile only aperiodically
A single tile that tile only aperiodically.
Whether a single tile exists that tiles only aperiodically is a is unsolved problem. Not anymore!
See: An aperiodic hexagonal tile (2010-03-22), By Joshua E S Socolar, Joan M. Taylor. arxiv.org 1003.4279v1.pdf
See also, some of my tiling studies: