Very nice links Yuzuha. But according to that study that I mentioned the garnet would still count as very low polygonity. I don't remember the number anymore but it was large (50 or 100?), each grain looked like it had tons of tiny little facets on it. I assume this is also why the flaky structure of natural waterstones works so well. Also, for experimental simplicity and to have access to more materials, they studied abrasion on a very soft material, not on steel, so that they could study the grooves after each swipe. Since many of the abrasives where not of geometrical shape but looked like (for the lack of a better description) spheres with tiny protrusions and they had to devise a clever mathematical model to assign to them a polygonity. Its been about 2 years since I read the article, so I am sorry that I am so vague, but I don't remember better. I simply remember that I filed that paper away in my brain under the category "very neat" but I also remember that the study was far from complete. They didn't study diamond either, I read about those somewhere else.
