  We propose a way to examine N=1 and N=2 string dualities on Calabi-Yau
three-folds or extensions. Our way is to find out or to construct two types of
toric representations of a Calabi-Yau three-fold, which contain phases
topologically equivalent or phases connected by flops. We discuss how to find
relations among Calabi-Yau three-folds realized in different toric
representations. We examine several examples of Calabi-Yau three-folds which
have the Hodge numbers, $(h^{1,1},h^{2,1})=(5,185)$ and the various numbers of
K3 fibers. We observe that each phase of our examples contains Del Pezzo
4-cycles, $B_8$ in six ways.
