A smaller version of Triple Gear is available here. A baseplate and axle for using a motor to move the triple gear is available here. Also see 15 cm axle for Triple gear and 30 cm axle for Triple gear.
In this unusual mechanism three gears mesh together in pairs, and yet they can turn!
If you take three ordinary gears and put them together so that each gear meshes with the other two, then none of the gears can turn because neighbouring gears must turn in opposite directions. Triple gear avoids this problem by having the three "gears" arranged like linked rings - the gears then rotate along skew axes, and the opposite direction rule no longer applies (although see also Oskar van Deventer's Magic Gears for another possible solution).
This is joint work with Saul Schleimer. We were inspired by another of Oskar's designs, his Knotted Gear, which consists of two linked rings that gear with each other, and of course we wondered if it would be possible to do three linked rings!
Here is a paper on the mathematics behind the Triple gear, and how we designed it.
A note on materials: I have so far printed it in White Strong & Flexible only. It may arrive with the rings slightly fused together, but gently moving them back and forth will loosen them up, and the mechanism gets smoother with use. I'm not sure what effect the polishing process would have on the gearing mechanism, since it would polish the exposed gear teeth but not those which are meshed as it comes out of the printer. So I have disabled the polished material options. If you really want to try it, let me know. I also haven't tested any of the "frosted detail" materials, but I imagine that they should work fine. It isn't printable in the other "detail" materials because of cleaning problems.
Here is a video showing how to loosen the gears (for the small version of the Triple gear, but the large is similar) if they arrive somewhat fused together.