Periodic diffraction from an aperiodic monohedral tiling.

Abstract

The diffraction pattern from the recently reported aperiodic `einstein', or `hat', monohedral tiling [Smith et al. (2023). arXiv:2303.10798v1] has been analyzed. The structure is the hexagonal mta net, a kite tiling, with aperiodic vertex deletions. A large model's diffraction pattern displays a robust sixfold periodicity in plane group p6. A repeating, roughly triangular motif of `diffused intensity' arises between the strongest Bragg peaks. The motif contains high-density regions of discrete `satellite' peaks, rather than continuous `diffuse scattering', breaking mirror symmetry, consistent with the chiral hat tiling.