Ditto... theory is that the thinner walls of the sides of the triangle (closest to the rifling in the barrel) would allow for optimum cooling whereas the thicker sides (the points of the triangles) would add great overall strength and rigidity to the barrel. this would "theoretically" give the benifits of both tapered and heavy barreled rifles.
warrants the question of weight comparison as one can only assume that the angled portions of the barrel would result in quite a bit of weight to allow for a barrel that is an equalateral triangle (even on all sides...)
simply put, if one were to think of it in terms of a bull barrel pulled down into a triangle, depending on the caliber, the original bull barrel would have to be quite large to result in an even triangular barrel once finished...so, though it would be lighter than the original (massive) bull barrel, it would still be quite heavy.