  Given a polyhedral cone sigma with smooth two-dimensional faces and,
moreover, a lattice point R in the dual cone of sigma, we describe the part of
the versal deformation of the associated toric variety TV(sigma) that is built
from the deformation parameters of multidegree R.
  Let Q the polyhedron obtained by intersecting sigma with the hyperplane R=1.
Then the base space is (the germ of) an affine scheme that reflects certain
possibilities of splitting Q into Minkowski summands.
