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