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Comment by king_geedorah | Hacker News Reader

Rather interesting solution to the problem. You can't test every possibility, so you pick one and get to rule out a bunch of other ones in the same region provided you can determine some other quality of that (non) solution.

I watched a pretty neat video[0] on the topic of ruperts / noperts a few weeks ago, which is a rather fun coincidence ahead of this advancement.

[0] https://www.youtube.com/watch?v=QH4MviUE0_s

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Not that coincidental. tom7 is mentioned in the article itself, and in his video's heartbreaking conclusion, he mentions the work presented in the article at the end. tom7 was working on proving the same thing!

And he tried to disprove the general conjecture, that every convex polyhedron has the Rupert property, by proving that the snub cube [1] doesn't have it. Which is an Archimedean solid and a much more "natural" shape than the Noperthedron, which was specifically constructed for the proof. (It might even be the "simplest" complex polyhedron without the property?)

So if he proves that the snub cube doesn't have the Rupert property, he could still be the first to prove that not all Archimedean solids have it.

1: https://en.wikipedia.org/wiki/Snub_cube

Wouldn’t this problem be related to the problem of finding whether two shapes collide in 3d space? That would probably be one of the most studied problems in geometry as simulations and games must compute that as fast as possible for many shapes.

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.

Wow this is such a well made video. So many great insights, just the right level of simplification and also funny as hell!

re-search :D

Truly a special gem of a channel.

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