The Osculatory Packing of a Three Dimensional Sphere

Abstract

Packings by unequal spheres in three dimensional space have interested many authors. This is to some extent due to the practical applications of such investigations to engineering and physical problems (see, for example, [ 16; 17; 31 ]). There are a few general results known concerning complete packings by spheres in N-dimensional Euclidean space, due mainly to Larman [ 20; 21 ]. For osculatory packings, although there is a great deal of specific knowledge about the two-dimensional situation, the results for higher dimensions, such as [ 4 ], rely on general methods which do not give particularly precise information.