Thank Berkeley robotics student Aaron Hoover for this mind-bending, one-sided gem.
Wired describes his difficult to convey contraption-
The white section is the Möbius strip and is flexible. It is made from silicone rubber, and has a twist, which means that — despite what your eyes and brain are telling you — it only has teeth along one side (because it only has one side).
The outer, black strip has a double twist that I still can’t make out after letting my eyes follow it around for a good 10 minutes now. Somehow, the little blue rubber “spur” gears guide these two impossible shapes and allow them to mesh. In theory, either the blue gears (planets, as this is essentially a planetary gear system) or the white “sun” strip can drive the movement. In practice, it’s easier to move the white strip by hand, and even then, the blue gears pop out occasionally.
I’m finding it hard to tear myself away from this picture, but I managed it for long enough to read Hoover’s detailed description of the planning and printing process (.pdf) from start to finish. It, too, is almost impossible to understand for a layman like me, but reading the nightmarishly complex calculations needed to make the gears line up makes this deceptively simple model seem even more impressive.