  We show that certain classes of K3 fibered Calabi-Yau manifolds derive from
orbifolds of global products of K3 surfaces and particular types of curves.
This observation explains why the gauge groups of the heterotic duals are
determined by the structure of a single K3 surface and provides the dual
heterotic picture of conifold transitions between K3 fibrations. Abstracting
our construction from the special case of K3 hypersurfaces to general K3
manifolds with an appropriate automorphism, we show how to construct Calabi-Yau
threefold duals for heterotic theories with arbitrary gauge groups. This
generalization reveals that the previous limit on the Euler number of
Calabi-Yau manifolds is an artifact of the restriction to the framework of
hypersurfaces.
