  A simple polytope $P$ is said to be \emph{B-rigid} if its combinatorial
structure is characterized by its Tor-algebra, and is said to be \emph{C-rigid}
if its combinatorial structure is characterized by the cohomology ring of a
quasitoric manifold over $P$. It is known that a B-rigid simple polytope is
C-rigid. In this paper, we, further, show that the B-rigidity is not equivalent
to the C-rigidity.
