I n pursuance of the F. NOŽIČKA'S paper [3] the question raises which dimension has a convex cone resp. generally a convex polyhedron, given by linear equations and inequalities. In the paper is described how to determine this dimension using the simplex method. One sees, that the problem in the main can be reduced to the finding of admissible basic solutions of a sequence of systems of linear equations and inequalities which are decreasing in size.