  Given a lattice polytope Q in R^n, we define an affine scheme M(Q) that
reflects the possibilities of splitting Q into a Minkowski sum. On the other
hand, Q induces a toric Gorenstein singularity Y, and we construct a flat
family over M(Q) with Y as special fiber. In case Y has an isolated singularity
only, this family is versal. (This revised version contains the proof now.)
