square pegs/ roundholes generalisation

It gets even more interesting when you generalize this problem to more than two dimensions!
(i.e. cubes-in-spheres/spheres-in-cubes and their higher dimensional equivalents). Which is the better fit
changes above 8 dimensions (Roughly speaking as you increase the number of dimensions, more and more of the volume of the hypercube is out near its corners - high dimension cubes are qualitatively more like hedgehogs than building blocks! )

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