Quote - Also, in regard to Path Tracing, the results of caustics and refraction of certain materials, like diamond, seemed much more believable when I actually defined the edges and facets with additional geometry.  This wasn't the case in unbiased render engines, like MentalRay, but it didn't actually hurt the results either.  So best to err on the side of caution.

I'm not totally surprised by this actually.  Unbiased, accurate path tracing techniques used for global light propagation, like the one in Octane, tend to expose low resolution objects for what they are... low resolution objects.  You might get black edges and faceted shadows on glass objects, or reflective surfaces, if you aren't using enough polys on an object.  This happens when the low poly surfaces are smooth shaded.  The common advice in the manuals of most of these render engines is to either define all the edges as hard, or subdivide the object until the prolem goes away.

I think you went a little overboard hardening the edges with extra edge loops in this model, but I can't argue that the render you created is just great, and that the model is very well done for the most part.  Personally, I think you could have just added one extra loop to the edges that you wanted to keep hard, and it would have been good enough.  Seems like you actually added several additional edges that probably weren't needed, even under the most extreme circumstances.  I don't know of any 3D software that would try that hard to smooth out those edges.  Even if the default smoothing was set to 180 degrees, two edge loops should be enough to deter it.

Your renders of the model are just jaw-dropping good, mate.  You nailed the materials perfectly.  Good work on the design too.  My only complaint is that it's a little gawdy for an engagement ring, unless you were marrying a female rapper.