Maximal triangulations of a regular prism

In this paper, we answer two conjectures of De Loera, Santos, and Takeuchi by demonstrating that the maximal size of a triangulation of a prism over a regular n-gon is ⌈n2+6n−164⌉, and that the maximal size of a regular triangulation of the regular n-antiprism is ⌊n2+8n−164⌋.