S-CONVEXITY, MODEL SETS AND THEIR RELATION

ZUZANA MASÁKOVÁ, JIŘÍ PATERA, AND EDITA PELANTOVÁ

Abstract. The relation of s-convexity and sets modeling physical quasicrystals is explained for quasicrystals related to quadratic unitary Pisot numbers. We show that 1-dimensional model sets may be characterized by s-convexity for finite set of parameters s. It is shown that the three Pisot numbers \frac{1}{2}(1 + \sqrt{5}), 1 + \sqrt{2}, and 2+\sqrt{3} related to experimentally observed non-crystallographic symmetries are exceptional with respect to s-convexity.