It depends on the ring size. One needs a lot more triangles to make up an US size 15 when compared to the number of triangles necessary to make up an US size 3.5. Both can use the same number of triangles, but because the size 15 is much larger this will make the triangular facets show up more readily. So the question is, what size are you interested in? If you give me a size or an inside diameter I can make up a file that I would consider to be the minimum number of triangles needed for polished silver. On the other hand, we tend to not worry about minimum facets since Shapeways can easily handle 1 million triangles without a problem. But then, were you wanting to print a large number of rings sprued together? Is that why you're asking?