2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209676We express the generating function for lattice points in a rational polyhedral cone with a simplicial subdivision in terms of multivariate analogues of the h-polynomials of the subdivision and "local contributions" of the links of its nonunimodular faces. We also compute new examples of nonunimodal h^*-vectors of reflexive polytopes.10 pages. v2: corrected attribution of Corollary 3.1, clarified computations in examples in Section 4, improved exposition. To appear in Discr. Comput. GeomCombinatorics52B20text