
Abstract: 
The sines of dimensional vertex angles of an simplex is defined and the law of sines for dimensional vertex angles of an simplex is established. Using the generalized sine law for simplex, we obtain some inequalities for the sines of dimensional vertex angles of an simplex. Besides, we obtain inequalities for volumes of simplices. As corollaries, the generalizations to several dimensions of the NeubergPedoe inequality and P. Chiakuei inequality, and an inequality for pedal simplex are given.;
