  In this paper, we show the existence of universal inequalities for the
$h^*$-vector of a lattice polytope P, that is, we show that there are relations
among the coefficients of the $h^*$-polynomial which are independent of both
the dimension and the degree of P. More precisely, we prove that the
coefficients $h^*_1$ and $h^*_2$ of the $h^*$-vector
$(h^*_0,h^*_1,\ldots,h^*_d)$ of a lattice polytope of any degree satisfy
Scott's inequality if $h^*_3=0$.
