  For the Traveling Salesman Polytope on n cities T_n, we construct its
approximation Q_k, k=1, 2, . . ., n^(1/3) using a projection of a polytope
whose number of facets is polynomial in n (of degree linear in k). We show that
T_n is contained in Q_k for each k, and that the scaling of Q_k by k/n+O(1/n)
is contained in T_n for each k. We show that certain facets of T_n lie on the
boundary of Q_k.
