PL-OM 1988 Problem 3

$W$ is a polygon which has a center of symmetry $S$ such that if $P$ belongs to $W$ , then so does $P'$ , where $S$ is the midpoint of $PP'$ . Show that there is a parallelogram $V$ containing $W$ such that the midpoint of each side of $V$ lies on the border of $W$ .