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In this paper, we consider the symmetric and Hankel-symmetric transportation polytope, which is the convex set of all symmetric and Hankel-symmetric non-negative matrices with prescribed row sum vector  R  and prescribed column sum vector  S . We characterize all extreme points of. Moreover, we show that the extreme points ofthe polytope of symmetric and Hankel-symmetric doubly stochastic matrices, can be obtained from the extreme points ofby specializing to the case that

Symmetric and Hankel-symmetric transportation polytopes