  We consider the minimization of an energy functional given by the sum of a
crystalline perimeter and a nonlocal interaction of Riesz type, under volume
constraint. We show that, in the small mass regime, if the Wulff shape of the
anisotropic perimeter has certain symmetry properties, then it is the unique
global minimizer of the total energy. In dimension two this applies to convex
polygons which are reflection symmetric with respect to the bisectors of the
angles. We further prove a rigidity result for the structure of (local)
minimizers in two dimensions.
