  We describe a class of isolated nondegenerate hypersurface singularities that
give a polynomial contribution to Batyrev's stringy E-function. These
singularities are obtained by imposing a natural condition on the facets of the
Newton polyhedron, and they are strictly canonical. We prove that Batyrev's
conjecture concerning the nonnegativity of stringy Hodge numbers is true for
complete varieties with such singularities, under some additional hypotheses on
the defining polynomials (e.g. convenient or weighted homogeneous). The proof
uses combinatorics on lattice polytopes. The results form a strong
generalisation of previously obtained results for Brieskorn singularities.
