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Random exploration of the three regular polytopes

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1 Author(s)
Blachman, Nelson M. ; GTE Gov. Syst. Corp., Mountain View, CA, USA

There are just three regular polytopes (the hypercube, cross polytope and the simplex) in Euclidean (n>4) space. We calculate their dimensions, including the distance from the centroid to the periphery in a random direction-that of a white Gaussian-noise vector. As n→∞, this distance becomes very predictable. It differs from the distance near which almost all of the volume and surface of the polytope lie

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Information Theory, IEEE Transactions on  (Volume:41 ,  Issue: 6 )