  In this paper, we classify the characteristic matrices associated to
quasitoric manifolds over a vertex cut of a finite product of simplices. We
discuss the integral cohomology rings of these quasitoric manifolds with
possibly minimal generators and show several relations among the product of
these generators. We classify integral cohomology rings (up to isomorphism as
graded rings) of the quasitoric manifolds over the vertex cut of a finite
product of simplices.
