Is there a reason to investigate this in three dimensions first? A lot of the questions (number of vertices, perimeter, area) make sense in two dimensions, and might be more tractable there. Andy On Fri, Mar 8, 2019 at 11:08 AM Allan Wechsler <acwacw@gmail.com> wrote:
Suppose we have a random point generator, that generates points in R^3 with all three coordinates normally distributed around 0, say with a standard deviation of 1, though it doesn't really matter.
Take N random points in this manner, and form the convex closure. This will be a polyhedron. What are the expected numbers of faces, vertices, and edges, in terms of N? Do they approach finite limits as N increases? I imagine that the surface area grows without bound. What about the expected number of faces that have 3, 4, 5, 6 edges, and so on?
I can think of many more questions of this sort, and am wondering if anybody here knows what's known. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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