A nopert polyhedron is a bounded convex polyhedron with nonempty interior that does not have Rupert's property. Thus no congruent copy can pass with positive clearance, without turning, through a straight tunnel cut in it. Such a convex polyhedron is also called non-Rupert (Steininger and Yurkevich 2025, Hervay 2026).
In terms of orthogonal projections, every choice of orientations and passage direction fails to place one projected copy strictly inside the other, even after a planar translation. Equivalently, its Nieuwland number is 1 (Hervay 2026).
Steininger and Yurkevich (2025) constructed the noperthedron, the first convex polyhedron proved to lack Rupert's property. Hervay (2026) gives a computer-assisted proof that the small rhombicosidodecahedron is also nopert, settling the conjecture of Steininger and Yurkevich (2023). An unsuccessful search over finitely many orientations alone does not prove that a convex polyhedron is nopert.
