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

We have previously shown, by redundant Klee-Minty constructions, that the central path may arbitrarily closely visit every vertex of the Klee-Minty cube. In those constructions, the redundant constraints are far away from the feasible region. In this paper, we provide a construction in which all redundant constraints touch the feasible region.