Abstract
Using the techniques of Gale diagrams a simple criterion is given for determining when a given spherical complex onS n−1 ⊂E 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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References
S. S. Cairns,Isotopic deformations of geodesic complexes on the 2-sphere and on the plane, Ann. of Math.45 (1944), 207–217.
B. Grünbaum,Convex Polytopes, London-New York-Sydney, 1967.
P. McMullen and G. C. Shephard,Convex Polytopes and the Upper Bound Conjecture, London Mathematical Society Lecture Notes, Vol. 3 (to be published).
G. C. Shephard,Diagrams for positive bases, J. London Math. Soc. (to be published).
F. Supnick,On the perspective deformation of polyhedra, Ann. of Math.49 (1948), 714–730 and53 (1951), 551–555.
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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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DOI: https://doi.org/10.1007/BF02771591