noperthedron (12. 693)

Via MetaFilter, we get the chance to revisit our favourite seventeenth century admiral and polymath Prince Rupert of the Rhein through a geometrical conjecture of his, a wager unsettled mathematically at the time, which may have been disproven. Having whittled out two identical cubes, Rupert wondered if one could cut a square shaped hole in one of the objects and pass the other through it, without breaking the original structure—the unit cube. Extrapolated into triangle shaped holes in pyramids and other polyhedra (all the Platonic solids, hypercubes, etc) were later demonstrated to possess “Rupertness” and can be shoved through each other—regardless of material—the edges kept intact and will even accommodate a shape slightly larger. Not cutting corners exactly, this bit of transdimensional engineering, shadow-casting turns the two-dimensional square into a rectangle in relation to the three-dimensional cube. Demonstrating the property was a long-standing challenge but modelling has been made simple through 3-D printing—see also. Recent studies, however, have shown but nope that the title polyhedron, a truncated convex figure with ninety vertices, made specifically for disproving the supposed universal attribute, is said to be not Rupert