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Let $C$ be a convex polytope in $\mathbb{R}^n$ with $m$ extremal points. Let $p\in \{1,2\}$. Can the $\ell^p$-projection $\Pi_C:\mathbb{R}^n\to C$ $$ \Pi_C(x) \in \operatorname{argmin}_{z\in C}\, \|x-...