  We derive the combinatorial representations of Picard group and deformation
space of anti-canonical hypersurfaces of a toric variety using techniques in
toric geometry. The mirror cohomology correspondence in the context of mirror
symmetry is established for a pair of Calabi-Yau (CY) ${\sf n}$-spaces in toric
varieties defined by reflexive polytopes for an arbitrary dimension ${\sf n}$.
We further identify the Kahler cone of the toric variety and degeneration cone
of CY hypersurfaces, by which the Kahler cone and degeneration cone for a
mirror CY pair are interchangeable under mirror symmetry. In particular,
different degeneration cones of a CY 3-fold are corresponding to flops of its
mirror 3-fold.
