Let
be a convex polyhedron with vertices
. Let
be the polyhedron obtained from
by a translation that moves
to
. Prove that at least two of the polyhedra
have an interior point in common.
%V0
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.
Školjka