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Update: problem reformulation Following the advice in comments, I now restate my problem using Voronoi tessellation. Given a unit hypercube $H_n=\{(x_1,\ldots,x_n)\in \mathbb{R}^n: 0\leq x_i\leq 1\}$...

I was motivated by this classical puzzle/1992 Putnam problem. Suppose 4 points are independently and uniformly distributed on a sphere in 3d. What is the probability the tetrahedron they form contains ...

This question is somewhat related to the question Intersecting cylinders, but where the cylinders are now modified to orbifolds in the hypercube with singularities occurring at the vertices of the ...