Five Essays on the Geometry of L\'aszl\'o Fejes T\'oth

Abstract

In this paper we consider the following topics related to results of L\'aszl\'o Fejes T\'oth: (1) The Tammes problem and Fejes T\'oth's bound on circle packings; (2) Fejes T\'oth's problem on maximizing the minimum distance between antipodal pairs of points on the sphere; (3) Fejes T\'oth's problem on the maximum kissing number of packings on the sphere; (4) The Fejes T\'oth -- Sachs problem on the one--sided kissing numbers; (5) Fejes T\'oth's papers on the isoperimetric problem for polyhedra.