The numbers of edges of the order polytope and the chain polytope of a finite partially ordered set

Let P be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope 풪(P) is equal to that of the chain polytope C(P). Furthermore, it will be shown that the degree sequence of the finite simple graph which is the 1-skeleton of 풪(P) is equal to that of C(P) if and only if 풪(P) and C(P) are unimodularly equivalent.