Tudor Zamfirescu

Discs held in cages

Abstract: A cage is the 1-skeleton of a convex polyhedron. More than half a century ago, Coxeter, Besicovitch, Aberth and Valette investigated 3-dimensional balls held by cages, and determined the minimal total length of those cages. In this talk we consider discs, i.e. 2-dimensional balls, held by cages, and try to determine the various positions the discs may have when being “almost fixed” by the cage. We shall determine the exact number of such positions for tetrahedral cages and the maximal number for pentahedral cages.