As many antipodes as vertices on convex polyhedra
Résumé
An earlier result states that, on the surface of a convex polyhedron with n vertices endowed with its intrinsic metric, a point cannot have more than n antipodes (farthest points). In this paper we produce examples of polyhedra with n vertices, on which some suitable point admits exactly n antipodes. We also proved that, for any positive number d ≤ 1, there exist (in the closure of the set of these polyhedra) some convex surfaces on which some point have a set of antipodes of Hausdorff dimension d.
Domaines
Sciences de l'environnement
Origine : Fichiers produits par l'(les) auteur(s)
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