Prince Rupert's cube: A cube can fit through a square hole drilled through another cube its size, or even slightly smaller. Now a Good Article on Wikipedia,

I've been wondering: is it possible to make Prince Rupert's Borromean rings, by drilling square holes into three unit cubes, each simultaneously passing through the hole in the next one?

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@11011110 I had to try it. Here's two nested cubes. It looks like a third one won't fit without intersecting I would say from eyeballing it.

3D viewer (and you can download the file): (CC BY-SA 4.0)

@timhutton I don't think the orientation of the hole from the optimal Prince Rupert cube solution (the one that allows the biggest cube to pass) will work, but that doesn't rule out the possibility of other holes with other orientations that work. There are a lot of choices to try: I think the only directions that you cannot drill a hole big enough to fit another cube through are the ones perpendicular to one of the coordinate axes.

@11011110 Sounds like a fun challenge. I guess you're thinking 'Borromean' because the three loops would likely be stuck inside each other and unable to slide apart?

@timhutton I guess what I mean is that you really have a structure, that is topologically a thickened set of Borromean rings, where each of the three rings has a cube as its convex hull. It's easy when you use slightly-non-uniform cuboids.

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