Convex Polytope Face

Last updated Nov 1, 2022

Let $V$ be an Inner Product Space over $\mathbb{R}$ and let $P \subset V$ be a Convex Polytope. Then a Set $F \subset P$ is a face of $P$ if any of the following is true:

1. $F = P$
2. $F = \emptyset$
3. there exists a Supporting Hyperplane $H \subset V$ so that $F = P \cap H$.

1. Characterization of Convex Polytope Faces

TODO - definition in terms of Valid Inequalitys.