Three dimensional line stochastic matrices and extreme points

Several properties of the extreme points of the convex set of three dimensional line stochastic matrices of order n are presented. The existence of many different classes of extremal configurations is established. These extremal matrices exhibit a large variety of patterns with some unexpected configurations. Latin squares of special types are used in some of the existence results. Furthermore, three questions raised by Brualdi and Csima are answered concerning the extreme points of three dimensional plane stochastic matrices of order n.