  In a previous study, we constructed a family of elliptic Calabi-Yau 4-folds
possessing a geometric structure that allowed them to be split into a pair of
rational elliptic 4-folds. In the present study, we introduce a method of
classifying the singularity types of this class of elliptic Calabi-Yau 4-folds.
In brief, we propose a method to classify the non-Abelian gauge groups formed
in four-dimensional (4D) $N=1$ F-theory for this class of elliptic Calabi-Yau
4-folds. To demonstrate our method, we explicitly construct several elliptic
Calabi-Yau 4-folds belonging to this class and study the 4D F-theory thereupon.
These constructions include a 4D model with two U(1) factors.
