Some results on centers of polytopes

The main ingredient for polynomiality in interior point methods is the centering procedure. All interior point algorithms for solving linear programming problems, known to be polynomial, has na explicit or implicit mechanism for finding a center of the linear programming polytope. Therefore, we consider the study of center of polytope as a serious work to be done. In this work, we want to talk about three kinds of centers of a polytope and its relations among them.