We systematically construct a large number of compact Calabi-Yau fourfolds
which are suitable for F-theory model building. These elliptically fibered
Calabi-Yaus are complete intersections of two hypersurfaces in a six
dimensional ambient space. We first construct three-dimensional base manifolds
that are hypersurfaces in a toric ambient space. We search for divisors which
can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations
over these base manifolds. We find that elementary conditions which are
motivated by F-theory GUTs lead to strong constraints on the geometry, which
significantly reduce the number of suitable models. The complete database of
models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out
several examples in more detail.Comment: 35 pages, references adde
