Geometric inequalities for simplices which are the simplest and the most useful polytopes have been a very attractive subject for a long time. Mitrinovic, Pecaric, Volenec [9], Ali [1], Gerber [4], Petty, Waterman [11] and other authors [7,8] have obtained a great number of elegant results. Specially, the quantity relations involving two simplices have been studied extensively. The well-known N...