Prince Rupert's Cube
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Pass a cube through another cube of equal size.
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- Math
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- Creative Commons — Attribution — Noncommercial
“Given two cubes of equal size, it is possible to bore a hole through one which is large enough to pass the other straight through." -Evan Scott, WWU, https://arxiv.org/abs/2208.12912
This is attributed to a bet made by Prince Rupert, and demonstrated by John Wallis.
https://en.wikipedia.org/wiki/Prince_Rupert%27s_cube#History
In fact, this is possible for any Platonic solid, and it has been conjectured to be possible for all convex polyhedra (Jerrard, Wetzel, Yuan 2017).
Don't believe? Just print it yourself and see. (It is a tight fit and the thin joints are delicate, so be gentle…)
Amaze your friends! Win a bet with Uncle Frank.
Support material is required for Rupert's Cube.
The .stl files are given in “ideal” printing orientation – for instance, Rupert's Cube is oriented so the thin joints are not along layer lines for a bit better strength (though they are still quite fragile). I printed one in TPU, and it's the only one I didn't break…
Last, it should be noted that this is not the optimal solution… This is using the solution of John Wallis, which assumes that the hole should be cut parallel to a one of the diagonals of the cube, but Pieter Nieuwland found the truly optimal solution by a slight rotation from the diagonal.