TRANSITION FROM SPHERICAL CIRCLE PACKING TO COVERING - GEOMETRICAL ANALOGS OF CHEMICAL ISOMERIZATION

How must n equal circles (spherical caps) of given angular radius r be arranged on the surface of a sphere so that the area covered by the c ircles will be as large as possible? In this paper, conjectured soluti ons of this problem for n = 5, 7, 8, 9, 10, 11 are given when r varies from the maximum packing radius to the minimum covering radius. The r elation of the results of this problem to the extremal configurations of n mutually repulsive equal point charges on the surface of a sphere is discussed. Variation of the solution polyhedra with r gives an abs tract model of chemical isomerization processes, for example for n = 5 where the packing --> covering transition models the Berry pseudo-rot ation of a trigonal bipyramid.