CICY3 Families of Nonsingular Codimension two K3

We conduct a systematic search of codimension 2 Complete Intersection Calabi–Yau threefolds (CICY3) in rank 2 toric ambient spaces and fibered by complete intersection of a quadric and a cubic in $\text{C}{\mathrm{\P }}^4$. We classify both the nonsingular ones as well as those with isolated singularities.