  We find that for many Calabi-Yau threefolds with elliptic or genus one
fibrations mirror symmetry factorizes between the fiber and the base of the
fibration. In the simplest examples, the generic CY elliptic fibration over any
toric base surface $B$ that supports an elliptic Calabi-Yau threefold has a
mirror that is an elliptic fibration over a dual toric base surface $\tilde{B}$
that is related through toric geometry to the line bundle $-6K_B$. The
Kreuzer-Skarke database includes all these examples and gives a wide range of
other more complicated constructions where mirror symmetry also factorizes.
Since recent evidence suggests that most Calabi-Yau threefolds are elliptic or
genus one fibered, this points to a new way of understanding mirror symmetry
that may apply to a large fraction of smooth Calabi-Yau threefolds. The
factorization structure identified here can also apply for Calabi-Yau manifolds
of higher dimension.
