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

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

Concerning the antipodality properties of finite sets, we focus on convex polytopes in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>...

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Bibliographic Details
Main Authors:	Rong Guo, Chan He, Longzhen Zhang, Senlin Wu
Format:	Article
Language:	English
Published:	MDPI AG 2025-04-01
Series:	Mathematics
Subjects:	Boltyanski’s illumination conjecture convex polytope antipodal points Hadwiger’s conjecture
Online Access:	https://www.mdpi.com/2227-7390/13/9/1412
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Summary:	Concerning the antipodality properties of finite sets, we focus on convex polytopes in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mn>3</mn></msup></semantics></math></inline-formula> with less than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>2</mn><mn>3</mn></msup></semantics></math></inline-formula> vertices and characterize convex polytopes with 5 vertices that are pairwise antipodal.
ISSN:	2227-7390