Estimates for the number of vertices of the polyhedron of polystochastic matrices

A multidimensional matrix is called polystochastic if it is non-negative and the sum of the elements in any of its lines is equal to 1. In the first half of the report we will make a short review of known estimates for the number of vertices of the polyhedron of polystochastic matrices (both of fixed dimension and fixed order), and in the second half of the report we will prove that the number of vertices of the polyhedron of polystochastic matrices of order 3 grows twice exponentially.