  Consider a complete intersection I of type (d_1,..., d_r) in a polynomial
ring over a field of characteristic 0. We study the graded system of ideals
{gin(I^n)}_n obtained by taking the reverse lexicographic generic initial
ideals of the powers of I and describe its asymptotic behavior. This behavior
is nicely captured by the limiting polytope which is shown to depend only on
the type of the complete intersection.
