On their project page [1] they even mention that there is a (infinite) family of shapes >> The hat is one member of a continuous family of shapes that are all

On their project page [1] they even mention that there is a (infinite) family of shapes >> The hat is one member of a continuous family of shapes that are all aperiodic, and that all tile the plane in the same way. [1] https://cs.uwaterloo.ca/~csk/hat/ https://cs.uwaterloo.ca/~csk/hat/