On the Bohemian Broadsword section of their website, Arms & Armor mentions that blades of this type were popular in the 12th and 13th centuries, and again in the 15th. Are they talking about the hexagonal blade section or the purpose of the sword as a primarily cutting weapon? Looking through Records of the Medieval Sword, I see a XIIa that looks like it has a hexagonal section, but the vast majority of this type of sword seem to be XIX's from the 15th and 16th centuries.

Also, is the blade type able to be more condusive towards thrusting? Making it stiffer by reducing the distal taper would make it very heavy, but many hexagonal sectioned swords already have a decent profile taper.

Anybody else interested in this most neglected of blade types? :)

I believe that A&A is referring to the blade's characteristic as a broad and flat instrument dedicated to the cut, not to the minutae of it's cross-section. Most blades of this type appear to have a flat lenticular cross-section although there are examples with hexagonal ones.