As many antipodes as vertices on some convex polyhedra

Joël Rouyer (1) , Tewfik Sari (1, 2)

1 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
2 MERE - Water Resource Modeling

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.

Mots clés: Antipode; convex polyhedron

Domaines: Géométrie métrique [math.MG]

Joël Rouyer, Tewfik Sari. As many antipodes as vertices on some convex polyhedra. 2009. ⟨hal-00465063⟩