  We prove that the number of vertices of a polytope of a particular kind is
exponentially large in the dimension of the polytope. As a corollary, we prove
that an n-dimensional centrally symmetric polytope with O(n) facets has
2^{Omega(n)} vertices and that the number of r-factors in a k-regular graph is
exponentially large in the number of vertices of the graph provided k >2r and
every cut in the graph with at least two vertices on each side has more than
k/r edges.
