DANZER-GRüNBAUM'S THEOREM REVISITED
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In this paper we prove some stronger versions of Danzer-Grünbaum's theorem including the following stability-type result. For 0 < α < 14π/27 the maximum number of vertices of a convex polyhedron in E 3 such that all angles between adjacent edges are bounded from above by α is 8. One of the main tools is the spherical geometry version of Pál's theorem.
KeywordsMain Tool Strong Version Spherical Geometry Convex Polyhedron Adjacent Edge
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