3 problems

Let $V\subset\mathbb R^3$ be an extremal set, and let $\mathcal B(V)$ be its Ball polytope. Call $V$ strongly critical if it has no proper subset which is extremal. Strong critical…

Let $P$ be a $3$-polytope, and let $V\subset\mathbb R^3$ be an extremal configuration; in fact, the source restricts to critical configurations. Write $\mathcal F(P)$ for the face…

Let $V\subset\mathbb R^3$ be an extremal configuration. Call $V$ strongly critical if no proper subset of $V$ is extremal. Let $\mathcal B(V)$ denote its Ball polytope, and conside…