Abstract. Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tilingcan be viewed as a substitution tiling. We use the substitution rule for this tiling and applythe algorithm of [1] to check overlap coincidence. It turns out that the tiling has overlap coinci-dence. So the tiling dynamics has pure point spectrum and we can conclude that this tiling has aquasicrystalline structure.Keywords: Mono-tile tiling, Quasicrystals, Pure point diffraction/dynamical spectrum, Self-affinetilings, Overlap coincidence. 1. IntroductionAperiodic tiles are the set of prototiles which tile the space with their isomorphic images byEuclidean motions (composition of translations, rotations and reflections) but only in non-periodicway. There have been many examples of aperiodic tiles and study on them [2, 4, 6, 11, 13, 24, 25, 28,29]. Two of well-known examples of aperiodic tiles with simple prototiles up to Euclidean motionsare Penrose tiles and Ammann tiles which are uncovered in the mid 70’s. These sets consist of twoprototiles and it has been the smallest number of prototiles which form aperiodic tiles until recently.Since then, people have been interested in finding a single prototile for an aperiodic tile. This problemis coined as ‘Mono-tile’ problem or ‘Einstein’ problem (one stone in German). It had taken quitesome time before Taylor and Socolar announced in 2010 the existence of an aperiodic mono-tile.Their tile is a hexagonal tile with colored decorations and matching rules which can be embeddedonto a single tile using shape only. Penrose had found earlier a mono-tile using matching rules whichis the reformulation of (1+ǫ+ǫ