  We use Batyrev-Borisov's formula for the generating function of stringy Hodge
numbers of Calabi-Yau varieties realized as complete intersections in toric
varieties in order to get closed form expressions for Hodge numbers of
Calabi-Yau threefolds in five-dimensional ambient spaces. These expressions
involve counts of lattice points on faces of associated Cayley polytopes. Using
the same techniques, similar expressions may be obtained for higher dimensional
varieties realized as complete intersections of two hypersurfaces.
