More bounds on the diameters of convex polytopes

Let Δ(d, n) be the maximum possible diameter of the vertex-edge graph over all d-dimensional polytopes defined by n inequalities. The Hirsch bound holds for particular n and d if Δ(d, n)≤n−d. Francisco Santos recently resolved a question open for more than five decades by showing that Δ(d, 2d)≥d+1 for d=43; the dimension was then lowered to 20 by Matschke, Santos and Weibel. This progress has stimulated interest in related questions. The …