  In the present paper we find a bijection between the set of small covers over
an $n$-cube and the set of acyclic digraphs with $n$ labeled nodes. Using this,
we give a formula of the number of small covers over an $n$-cube (generally, a
product of simplices) up to Davis-Januszkiewicz equivalence classes and
$\mathbf{Z}^n$-equivariant diffeomorphism classes. Moreover we prove that the
number of acyclic digraphs with $n$ unlabeled nodes is an upper bound of the
number of small covers over an $n$-cube up to diffeomorphism.
