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 - 16/4], and that the maximal size of a regular triangulation of the regular n-antiprism is [n2 + 8n - 16/4].