  We study, as hypersurfaces in toric varieties, elliptic Calabi-Yau fourfolds
for F-theory compactifications dual to E8xE8 heterotic strings compactified to
four dimensions on elliptic Calabi-Yau threefolds with some choice of vector
bundle. We describe how to read off the vector bundle data for the heterotic
compactification from the toric data of the fourfold. This map allows us to
construct, for example, Calabi-Yau fourfolds corresponding to three generation
models with unbroken GUT groups. We also find that the geometry of the
Calabi-Yau fourfold restricts the heterotic vector bundle data in a manner
related to the stability of these bundles. Finally, we study Calabi-Yau
fourfolds corresponding to heterotic models with fivebranes wrapping curves in
the base of the Calabi-Yau threefolds. We find evidence of a topology changing
extremal transition on the fourfold side which corresponds, on the heterotic
side, to fivebranes wrapping different curves in the same homology class in the
base.
