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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 co…
The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution. Here Greg Egan shows how Rupert’s property works for the cube: The triakis tetrahedron is an extremely close call, but it does have Rupert’s property:
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