The universal Rupert conjecture for convex polyhedra

A convex polyhedron is a polyhedron in $\operatorname{\mathbb{R}}^3$ whose faces are convex polygons. Such a polyhedron has Rupert's property if a hole can be cut into it through which a congruent copy of the polyhedron can pass. Universal Rupert conjecture. Every convex polyhedron has Rupert's property. This is a longstanding open problem motivated by the fact that all five Platonic solids and all but three of the Archimedean solids are known to be Rupert.