Jerrad et al.'s conjecture that every convex polyhedron is Rupert

A Rupert compact convex set $S\subseteq\mathbb{R}^3$ admits a passage in which a second copy of $S$ passes straight through a hole in the interior of the first, with rescaling factor $\mu_S>1$. The Nieuwland constant $\mu_S$ is the largest possible rescaling factor for such a passage. Jerrad et al.'s conjecture. Every convex polyhedron in $\mathbb{R}^3$ is Rupert. The conjecture asks whether the Rupert property holds universally for three-dimensional convex polyhedra; the paper notes that the unit ball is not Rupert and that several Archimedean and Catalan solids remain unresolved.