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 hete
rotic duals are determined by the structure of a single K3 surface and
provides the dual heterotic picture of conifold transitions between K
3 fibrations. Abstracting our construction from the special case of K3
hypersurfaces to general K3 manifolds with an appropriate automorphis
m, we show how to construct Calabi-Yau threefold duals for heterotic t
heories with arbitrary perturbative gauge groups. This generalization
reveals that the previous limit on the Euler number of Calabi-Yau mani
folds is an artifact of the restriction to the framework of hypersurfa
ces.