  The degree zero part of the quantum cohomology algebra of a smooth Fano toric
symplectic manifold is determined by the superpotential function, W, of its
moment polytope. In particular, this algebra is semisimple, i.e. splits as a
product of fields, if and only if all the critical points of W are
non-degenerate. In this paper we prove that this non-degeneracy holds for all
smooth Fano toric varieties with facet-symmetric duals to moment polytopes.
