  To r ideals on a germ of smooth variety X one attaches a rational polytope in
the r-dimensional Euclidean space (the LCT-polytope) that generalizes the
notion of log canonical threshold in the case of one ideal. We study these
polytopes, and prove a strong form of the Ascending Chain Condition in this
setting: we show that if a sequence P_m of such LCT-polytopes converges to a
compact subset Q in the Hausdorff metric, then Q is equal to the intersection
of all but finitely many of the P_m. Furthermore, Q is an LCT-polytope.
