In my constant quest for the best unique wedding band, I also came across the Mobius Eternity ring by Christina Kober, an Atlanta-based jeweler.
Her Etsy page says of the ring:
A mobius strip is a cool geometric phenomena, first discovered by a German mathematician, August Ferdinand Möbius. It is a two-dimensional structure with only one side. This means that like a ring, which has no beginning or end, a mobius strip has no "inside" or "outside", but has only one, continuous "side".
A mobius strip is a representation of eternity, because it is endless and on going.