  We discuss some aspects of F-theory in four dimensions on elliptically
fibered Calabi-Yau fourfolds which are Calabi-Yau threefold fibrations. A
particularly simple class of such manifolds emerges for fourfolds in which the
generic Calabi-Yau threefold fiber is itself an elliptic fibration and is K3
fibered. Duality between F-theory compactified on Calabi-Yau fourfolds and
heterotic strings on Calabi-Yau threefolds puts constraints on the cohomology
of the fourfold. By computing the Hodge diamond of Calabi-Yau fourfolds we
provide first numerical evidence for F-theory dualities in four dimensions.
