3 problems

A planar, 3-connected graph $G$ is strongly self-dual if it has a self-duality isomorphism $\tau:G\to G^*$ such that, for every pair of vertices $u,v$, $u\in\tau(v)$ if and only if…

Let $G=(V,E)$ be an involutive polyhedral graph: a self-dual polyhedral graph equipped with an involution $\tau$ satisfying $v\notin\tau(v)$ and $u\in\tau(v)\iff v\in\tau(u)$. A Re…

Let $V\subset\mathbb{R}^3$ be an extremal set for the frequent large distance problem, and let $\mathcal{B}(V)$ denote the associated ball polyhedron. The set $V$ is strongly criti…