In this paper, a procedure is developed to construct compact F-theoryfourfolds corresponding to perturbative IIB O7/O3 models on CICY threefoldswith permutation involutions. The method is explained in generality, and thenapplied to specific examples where the involution permutes two Del Pezzosurfaces. The fourfold construction is successfully tested by comparing the D3charges predicted by F-theory and IIB string theory. The constructed smoothfourfolds are then taken to the locus in moduli space where they have enhancedSU(5) singularities. A general, intuitive method is developed for engineeringthe desired singularities in Weierstrass models for complicated D7-branesetups.
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