A Rupert polyhedron is a bounded convex polyhedron with nonempty interior and Rupert's property, meaning that a congruent copy can pass with positive clearance, without turning, through a straight tunnel cut in it (Steininger and Yurkevich 2023).
A convex polyhedron is Rupert iff two of its orthogonal projections can be placed with one strictly inside the other using a planar rotation and translation. For a convex polyhedron that is a centrosymmetric set, the projected centers may be taken to coincide, so the translation can be omitted (Steininger and Yurkevich 2023).
All five Platonic solids are Rupert (Jerrard et al. 2017). Steininger and Yurkevich (2023) established the property for ten of the thirteen Archimedean solids. A convex polyhedron without the property is a nopert polyhedron.
