Rupert's Property
13 days ago
- #polyhedron
- #Rupert’s property
- #geometry
- A hole can be cut in a cube large enough to slide an identical cube through it, known as Rupert’s property.
- Steininger and Yurkevich proved the existence of a convex polyhedron (90 vertices, 240 edges, 152 faces) that lacks Rupert’s property, named 'noperthedron'.
- The proof involved a computer search of 18 million different holes and additional mathematical verification.
- Prince Rupert’s cube is named after Prince Rupert of the Rhine, who first posed the problem of passing a cube through another cube of the same size.
- John Wallis provided a positive answer, and Pieter Nieuwland later found the largest possible cube that can pass through a unit cube.
- Greg Egan and David Renshaw demonstrated Rupert’s property for various polyhedra, including the cube and regular octahedron.
- The triakis tetrahedron narrowly has Rupert’s property.