More bounds on the diameter of convex polytopes

Let ∆(d, n) be the maximum possible edge diameter over all d-dimensional polytopes defined by n inequalities. The Hirsch conjecture, formulated in 1957, suggests that ∆(d, n) is no greater than n − d. No polyno-mial bound is currently known for ∆(d, n), the best one being quasi-polynomial due to Kalai and Kleitman in 1992. Goodey showed in 1972 that ∆(4, 10) = 5 and ∆(5, 11) = 6, and more recently, Bremner and Schewe showed ∆(4, 11) = ∆(6, 12) = 6. In this follow-up, we show tha