We are given a set of magnitude of vectors. These vectors are free to move and rotate in space. How can we verify that whether this set of given vectors form a polytope?
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1Do you really mean the whole polytope? Or could you mean the vertices of a convex polytope? In the latter case, such a polytope always exists, for any finite set of lengths. – Aug 05 '13 at 00:52
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2Do you mean whether a finite list of positive real numbers are the edge-lengths of some 3-dimensional polytope? – Aug 05 '13 at 07:04