A test for this one is a bit simpler, I think, because you just have to find a 2D projection of the shape from multiple orientations so one fits inside the other. You don't technically have to do any 3D comparisons beyond the projections.
It's pretty easy to brute force most shapes to prove the property true. The challenge is proving that a shape does not have the Rupert property, or that it does when it's a very specific and tight fit. You can't test an infinite number of possibilities.
It's pretty easy to brute force most shapes to prove the property true. The challenge is proving that a shape does not have the Rupert property, or that it does when it's a very specific and tight fit. You can't test an infinite number of possibilities.