Shephard's problem (a.k.a. Dürer's conjecture)

In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane that can be folded to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard.