A redundant Klee-Minty construction with all the redundant constraints touching the feasible region

By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geometrically. In this paper, we provide a new construction in which all of the distances are set to zero, i.e., all of the redundant constraints touch the feasible region.