A Characterization of Three-Dimensional Convex Polytopes with Five Pairwise Antipodal Vertices

Rong Guo, Chan He, Longzhen Zhang and Senlin Wu ()
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Rong Guo: School of Mathematics, North University of China, Taiyuan 030051, China
Chan He: School of Mathematics, North University of China, Taiyuan 030051, China
Longzhen Zhang: School of Mathematics, North University of China, Taiyuan 030051, China
Senlin Wu: School of Mathematics, North University of China, Taiyuan 030051, China

Mathematics, 2025, vol. 13, issue 9, 1-14

Abstract: Concerning the antipodality properties of finite sets, we focus on convex polytopes in R 3 with less than 2 3 vertices and characterize convex polytopes with 5 vertices that are pairwise antipodal.

Keywords: Boltyanski’s illumination conjecture; convex polytope; antipodal points; Hadwiger’s conjecture (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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