Q: Brute-force vertex enumeration for polytope Let $P$ be a polytope of $\mathbb{R}^n$ defined by a (bounded) finite family of half-spaces $t_i \cdot x \leq q_i$ with every $t_i \in \mathbb{R}^n$ non-zero and $q \in \mathbb{R}$. There is no assumption on $P$ being full-dimensional or that the family of half-spaces is irredundant.
Consider every intersection of bounding hyperplanes of these half-spaces, for which the intersection has dimension zero, i.e. is a single point. Discard every such singleton that is not contained in $P$.
Does the resulting singletons constitute precisely the vertices of $P$?
