A Convex Polyhedron That Defies Intuition: No Rupert's Property
2025-08-29
For a long time, it was believed that any convex polyhedron could have a hole cut through it large enough to pass an identical copy through. This is known as 'Rupert's property'. This week, Steininger and Yurkevich proved this wrong! They found a convex polyhedron with 90 vertices, 240 edges, and 152 faces that lacks this property. Their proof involved a computer search of 18 million possible holes, combined with rigorous mathematical arguments. They dubbed this counter-example a 'noperthedron'. This discovery challenges long-held assumptions in geometry.
Misc
polyhedron