s-convexity, model sets and their relation
Zuzana Masáková, Jirí Patera, and Edita Pelantová
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 $\frac12(1+\sqrt5)$, $1+\sqrt2$, and $2+\sqrt3$ related to experimentally observed non-crystallographic symmetries are exceptional with respect to $s$-convexity.