## apply piecewise linear function to vertices of polytope while remaining in facet representation

Let $P \subseteq \mathbb{R}^d$ be a polytope with vertices $V$, and let $f$ be a function $\mathbb{R}^d \to \mathbb{R}$.

Let $P’ \subseteq \mathbb{R}^{d+1}$ be the polytope with vertices $\{(v, f(v)) \; \forall v \in V \}$

…