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Spherical complexes and radial projections of polytopes

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Abstract

Using the techniques of Gale diagrams a simple criterion is given for determining when a given spherical complex onS n−1E n is the radial projection, from the centre ofS n−1, of a convex polytope. Previously a criterion was known only for the casen=2.

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Shephard, G.C. Spherical complexes and radial projections of polytopes. Israel J. Math. 9, 257–262 (1971). https://doi.org/10.1007/BF02771591

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