  We construct, as hypersurfaces in toric varieties, Calabi-Yau manifolds
corresponding to F-theory vacua dual to E8*E8 heterotic strings compactified to
six dimensions on K3 surfaces with non-semisimple gauge backgrounds. These
vacua were studied in the recent work of Aldazabal, Font, Ibanez and Uranga. We
extend their results by constructing many more examples, corresponding to
enhanced gauge symmetries, by noting that they can be obtained from previously
known Calabi-Yau manifolds corresponding to K3 compactification of heterotic
strings with simple gauge backgrounds by means of extremal transitions of the
conifold type.
