  In 1694, Gregory and Newton proposed the problem to determine the kissing
number of a rigid material ball. This problem and its higher dimensional
generalization have been studied by many mathematicians, including Minkowski,
van der Waerden, Hadwiger, Swinnerton-Dyer, Watson, Levenshtein, Odlyzko,
Sloane and Musin. In this paper, we introduce and study a further
generalization of the kissing numbers for convex bodies and obtain some exact
results, in particular for balls in dimensions three, four and eight.
