  There is a simple formula for the Ehrhart polynomial of a cyclic polytope.
The purpose of this paper is to show that the same formula holds for a more
general class of polytopes, lattice-face polytopes. We develop a way of
decomposing any d-dimensional simplex in general position into d! signed sets,
each of which corresponds to a permutation in the symmetric group, and reduce
the problem of counting lattice points in a polytope in general position to
that of counting lattice points in these special signed sets. Applying this
decomposition to a lattice-face simplex, we obtain signed sets with special
properties that allow us to count the number of lattice points inside them. We
are thus able to conclude the desired formula for the Ehrhart polynomials of
lattice-face polytopes.
