  It is shown that, for each $d \geq 4$, there exists an integral convex
polytope $\mathcal{P}$ of dimension $d$ such that each of the coefficients of
$n, n^{2}, \ldots, n^{d-2}$ of its Ehrhart polynomial $i(\mathcal{P},n)$ is
negative. Moreover, it is also shown that for each $d \geq 3$ and $1 \leq k
\leq d-2$, there exists an integral convex polytope $\mathcal{P}$ of dimension
$d$ such that the coefficient of $n^k$ of the Ehrhart polynomial
$i(\mathcal{P},n)$ of $\mathcal{P}$ is negative and all its remaining
coefficients are positive. Finally, we consider all the possible sign patterns
of the coefficients of the Ehrhart polynomials of low dimensional integral
convex polytopes.
