Explore the second part of a mathematical conference talk examining Lagrangian torus fibrations on Calabi-Yau toric hypersurfaces with discriminant in codimension 2. Delve into the combinatorial aspects of constructing the potential function and understand how it achieves a delicate balance between strict convexity and linearity. Learn about the resulting integral affine structure in the base of the fibration, with particular emphasis on the positioning of the discriminant. This presentation builds upon joint research with Mak Matessi-Ruddat that proves the existence of these important geometric structures. The talk was delivered as part of the "New Developments in Singularity Theory" conference, a joint IMSA & ICMS event supported by the Simons Foundation, National Science Foundation, and the University of Miami.