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I'm a physics masters student and working on a subject where I have to create some random polyhedra for some purpose. I devised an algorithm to create polyhedra by assigning points on the surface of an ellipsoid, but someone told me that this causes a tough restriction on the formed polyhedra.

Actually I can't believe this, I also have a feeling that there's some theorem that would say that every polyhedron may be inscribed in an ellipsoid, is that true? could anyone please tell me where to read to understand whether this is a restriction or not?

Thank you,

Samer