A lower bound for the translative kissing numbers of simplices

The translative kissing number H(K) of a d-dimensional convex body K is the maximum number of mutually non;overlapping translates of K that can be arranged so that all touch K. In this paper we show that H(S-d) greater than or equal to 1.13488((1-o(1))d) holds for any d-dimensional simplex S-d (d greater than or equal to 1). We also prove similar inequalities for some, more general classes of convex bodies.