Rupert’s property: cut a hole in a polyhedron big enough for an identical copy to slide through

Mathematicians have solved a puzzle about whether all convex polyhedra have "Rupert's property"—allowing an identical copy to slide through a hole cut in them. Steininger and Yurkevich proved that a specific 90-vertex polyhedron, dubbed the "noperthedron," lacks this property. Their proof involved examining 18 million potential holes using complex math. This discovery disproves the conjecture that all convex polyhedra might possess Rupert's property, which was known to exist in cubes, octahedra, and many other polyhedra.