Mathematicians Prove Existence of Polyhedron Without Rupert's Property
By
robinhouston
Fresh out the oven, still warm. Top of the tray.
Summary
Researchers Steininger and Yurkevich have proven the existence of a convex polyhedron that cannot have a hole cut through it large enough to pass the entire shape through itself, solving a long-standing mathematical problem known as 'Rupert's property'. The polyhedron has 90 vertices, 240 edges, and 152 faces, and the proof required a computer search of 18 million different configurations. This breakthrough resolves a mathematical mystery where previously it was known that cubes and other shapes could pass through holes in themselves, but no convex polyhedron had been proven incapable of this property.
Key quotes
· 5 pulledYou can cut a hole in a cube that's big enough to slide an identical cube through that hole!
Amazingly, nobody could prove any convex polyhedron doesn't have this property!
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 prove that no such hole is possible, they had to do a computer search of 18 million different configurations.
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