  Let $P$ be a cubic $3$-connected bipartite plane graph which has a $2$-factor
which consists only of facial $4$-cycles, and suppose that $P^{*}$ is the dual
graph. We show that $P$ has at least $3^{\frac{2|P^{*}|}{\Delta^{2}{(P^{*})}}}$
different Hamilton cycles.
