  We show that the Ehrhart h-vector of an integer Gorenstein polytope with a
regular unimodular triangulation satisfies McMullen's g-theorem; in particular,
it is unimodal. This result generalizes a recent theorem of Athanasiadis
(conjectured by Stanley) for compressed polytopes. It is derived from a more
general theorem on Gorenstein affine normal monoids M: one can factor K[M] (K a
field) by a "long" regular sequence in such a way that the quotient is still a
normal affine monoid algebra. This technique reduces all questions about the
Ehrhart h-vector of P to the Ehrhart h-vector of a Gorenstein polytope Q with
exactly one interior lattice point, provided each lattice point in a multiple
cP, c in N, can be written as the sum of n lattice points in P. (Up to a
translation, the polytope Q belongs to the class of reflexive polytopes
considered in connection with mirror symmetry.) If P has a regular unimodular
triangulation, then it follows readily that the Ehrhart h-vector of P coincides
with the combinatorial h-vector of the boundary complex of a simplicial
polytope, and the g-theorem applies.
