[math-fun] Octocog

This problem impinged during my customary brainstorming session in search of convincing reasons not to get out of bed. I have not examined it, so have no idea whether it is well-known, easy, hard or impossible. Deventer's "Gear Shift" puzzle http://www.jaapsch.net/puzzles/gearshift.htm is topologically equivalent to an octahedron with a gear on each face, meshing with three gears adjacent at edges. Is it possible to morph this concept into its planar map: a flat train comprising one ring enclosing two 3-planet tiers around one sun? Furthermore, do such trains exist with 6-fold, 2-fold, and no symmetry? Fred Lunnon