Abstract
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.
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Bezdek, K., Blekherman, G. DANZER-GRüNBAUM'S THEOREM REVISITED. Periodica Mathematica Hungarica 39, 7–15 (2000). https://doi.org/10.1023/A:1004878520642
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DOI: https://doi.org/10.1023/A:1004878520642