  In this article, we consider the phenomenon of complete coincidence of the
key properties of pairs of Calabi-Yau manifolds realized as hypersurfaces in
two different weighted projective spaces. More precisely, the first manifold in
such a pair is realized as a hypersurface in a weighted projective space, and
the second as a hypersurface in the orbifold of another weighted projective
space. The two manifolds in each pair have the same Hodge numbers and special
K\"ahler geometry on the complex structure moduli space and are associated with
the same $N=2$ gauge linear sigma model. We give the explanation of this
interesting coincidence using the Batyrev's correspondence between Calabi-Yau
manifolds and the reflexive polyhedra.
