  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.
