Cool paper!
[EDIT: The following is my own clumsy mistake] Minor note: The definition of "mean width" of a polyhedron P in the paper is not translation invariant, and that's confusing. In other words, the mean width of a polyhedron P can differ from that of P+x := {p+x | p ∈ P} where x is some vector. Is that intended? It doesn't agree with how the word "width" is normally used. I would call it a "mean furthest projection". Or maybe "mean peak projection" or "mean shadow"?
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