Klee-Minty cube ($0\le x_1\le 1,\epsilon x_{j-1}\le x_j\le 1-\epsilon x_{j-1}$)

For $0<\epsilon <1/2$, these inequalities define a deformed cube with $2^n$ vertices of a polytope. Choose either the lower or upper bound recursively at each coordinate to obtain a vertex of a polytope; changing one choice gives an adjacent vertex of a polytope. When maximizing $x_n$, smallest-index improving-facet pivoting visits all $2^n$ vertices of a polytope: first traverse the lower last-coordinate face, then move to the upper face and traverse the preceding path in reverse. Thus this geometric version of the Bland pivoting rule can require $2^n-1$ pivots. Rescaling the coordinate $x_i$ to $y_i={\epsilon }^{2(n-i)}{x}_i$ makes the positive rate per unit freed coordinate equal to ${\epsilon }^{-(n-i)}$; Dantzig pivot rule then selects the same exponential path. Euclidean edge-length pricing is a different rule.