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.
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