IMO 1971 Problem 2

Let $P_1$ be a convex polyhedron with vertices $A_1,A_2,\ldots,A_9$ . Let $P_i$ be the polyhedron obtained from $P_1$ by a translation that moves $A_1$ to $A_i$ . Prove that at least two of the polyhedra $P_1,P_2,\ldots,P_9$ have an interior point in common.