Sterling silver, cubic zirconia
A few years ago, I had a discussion with the designers and merchants at a mom-and-pop jewelry store in Honolulu about how to achieve a look similar to that of an invisible setting without actually using specially-grooved princess-cut stones. Invisible settings are the crème de la crème of pavé settings in that no metal shows between stones, and the uniformity of the both the surface and stone sizes creates an unparalleled smoothness to the touch and a whole heck of a lot of bling. The difficulties with the technique are that the metal substructure that the stones snap into isn't as secure as other methods of setting, and it's a patented process so it comes with licensing fees.
I suggested that the best way to approach the challenge would be to create a grid of asscher-cut stones. Asschers have notched corners which would allow them to be set with shared prongs in a more traditional pavé fashion, but would also share their longer edges with other stones like a princess cut. True, you would see some metal, but there would be more edge-to-edge diamond than visible prong and thus the effect would be very similar to that of an invisible setting. They rejected the idea in favor of a simpler technique that used small round stones to mostly fill the gaps between larger round stones—it was a beautiful look, but it didn't at all achieve the originally-stated design goal.
I finally decided to put my own idea to the test—and as you can see from the result, the effect is exceptional. Despite the prongs, the edge-to-edge mating of each stone provides a uniformity and brilliance that is second only to the style it's approximating, and the prongs have been pushed low enough that there is no tactile disturbance when running one's fingers along the surface of the pavé.
Since this was an initial experiment, I opted to set forty 3mm asscher-cut CZs in a silver ring rather than a more expensive combination of materials—but I'm happy to reproduce this in gold and diamonds or other gem/metal options on request. I'll be sure to use the technique in future pieces, as well, now that it's a proven concept that can be applied to other designs.