Approximate Labelling for Simplicial Algorithms and Two Classes of Special Subsets of the Sphere

Call a subset of Rn complete if the origin is in its convex hull. We are concerned with the construction of large finite sets of points on the unit sphere whose complete subsets are, in some sense, easy to describe. Our motivation comes from simplicial algorithms for approximating zeroes of functions. We construct two classes of such subsets of the sphere, both of which generalize a subset that corresponds to usual integer labelling.

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