28623 articles – 22140 references  [version française]

hal-00465063, version 1

As many antipodes as vertices on some convex polyhedra

Joël Rouyer () 1, Tewfik Sari () 1, 2

(2009-09-24)

Abstract: An earlier result states that a point of the surface of a convex polyhedron with n vertices, endowed with its intrinsic metric, cannot have more that n antipodes (farthest points). In this paper we produce examples of polyhedra with n vertices on which some suitable point admits exactly n antipodes.

  • 1:  Laboratoire de Mathématiques Informatique et Applications (LMIA)
  • Université de Haute Alsace - Mulhouse
  • 2:  MERE (INRIA Sophia Antipolis - INRA/SupAgro UMR 0729 MISTEA - Montpellier)
  • INRIA – Institut national de la recherche agronomique (INRA) : UMR0729
  • Domain : Mathematics/Metric Geometry
  • Keywords : Antipode – convex polyhedron
 
  • hal-00465063, version 1
  • http://hal.archives-ouvertes.fr/hal-00465063
  • oai:hal.archives-ouvertes.fr:hal-00465063
  • From: Tewfik Sari <>
  • Submitted on: Thursday, 18 March 2010 18:28:02
  • Updated on: Friday, 19 March 2010 13:42:50