  In this paper, a procedure is developed to construct compact F-theory
fourfolds corresponding to perturbative IIB O7/O3 models on CICY threefolds
with permutation involutions. The method is explained in generality, and then
applied to specific examples where the involution permutes two Del Pezzo
surfaces. The fourfold construction is successfully tested by comparing the D3
charges predicted by F-theory and IIB string theory. The constructed smooth
fourfolds are then taken to the locus in moduli space where they have enhanced
SU(5) singularities. A general, intuitive method is developed for engineering
the desired singularities in Weierstrass models for complicated D7-brane
setups.
