As many antipodes as vertices on convex polyhedra
| Pas de texte intégral | |
|---|---|
| Auteurs |
Joel Rouyer Tewfik Sari |
| Unité de recherche du site |
Laboratoire Mathématiques, Informatique et Applications - LMIA - EA3993 |
| Langue |
en |
| Volume |
12 |
| Numéro |
1 |
| Page de début |
43 |
| Page de fin |
61 |
| Date de première publication |
2012-03-31 |
| Date de parution |
2012 |
| ISSN |
1615-715X |
| Titre de la source (revue, livre…) |
Advances in Geometry |
| 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 Show moreAn 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 71 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 has a set of antipodes of Hausdorff dimension d. Show less |
| DOI | 10.1515/advgeom.2011.030 |
| Éditeur |
De Gruyter |
| URL éditeur |
http://www.degruyter.com/view/j/advg.2012.12.issue-1/advgeom.2011.030/advgeom.2011.030.xml?format=INT |
| Type de publication |
journal article |
| Type de publication |
ACL |
| Topic |
Mathématiques [math]/Mathématiques générales [math.GM] |
| Mots-clés |
convex polyhedra |
| Fonction |
aut |
| Identifiant idREF |
095778101 |
| Audience |
International |
| URL | https://univoak.eu/islandora/object/islandora:32850 |