More polytopes meeting the conjectured Hirsch bound

In 1957 W.M. Hirsch conjectured that every d-polytope with n facets has edge-diameter at most n ? d. Recently Holt and Klee constructed polytopes which meet this bound for a number of (d; n) pairs with d 13 and for all pairs (14; n). These constructions involve a judicious use of truncation, wedging, and blending on polytopes which already meet the Hirsch bound. In this paper we extend these techniques to construct poly-topes of edge-diameter n ? 8 for all (8; n). The improvement from d = 14 to d = 8 follows from identifying circumstances in which the results for wedging when n > 2d can be extended to the cases n 2d, our lemma 2.2.