This ring was created with ShapeJS, a programming language made by Shapeways. The ring is the combination of two bands. The inner band (size 9.5 19.4 mm diameter) is 1.5 mm thick and provides a smooth surface. The outer band is made by intersecting a SchwarzD Minimal Surface with the outer band, a ring. As before, minimal surfaces are the minimal surface needed to connect given boundary conditions (like soap bubbles forming inside a ring of wire or a circus tent draped on poles. Here the minimal surface provides a quick way to make an interesting pattern. After the intersection, the corners are rounded. Currently the minimum feature size is 1mm thick, so sharp corners or very thin features need to be smoothed out for printing. To help with printing I made the SchwarzD pattern very thin with a larger period. It is not easy to get a sense of the minimal surface from the final ring design, but the pattern it produces is interesting. It reminds me of waves in sand. Here is a link to the ShapeJS minimal surface ring example.
SchwarzD ring is now available on my Shapeways store.