Rupert's Property
You can cut a hole in a cube that’s big enough to slide an identical cube through that hole! Think about that for a minute—it’s kind of weird. Amazingly, nobody could prove any convex polyhedron doesn’t have this property! It’s called ‘Rupert’s property’. Until this week. This week Steininger and Yurkevich proved there is a convex polyhedron that you can’t cut a hole in big enough to slide the entire polyhedron through the hole. It has 90 vertices, and apparently 240 edges and 152 faces. To