Any time two planes overlap (read: are not parallel), they overlap in one of four different ways: cranes, butterflies, atoms, or tangles. In the first three arrangements, it's possible to keep the poi rotating without interfering with each other. I'm pretty sure that any and all tangles result from the final atom shape. Here's a handy-dandy diagram that breaks this down in an easy-to-read fashion: http://www.drexfactor.com/sites/default/files/atomicclashes.jpg

techblog294.mp4

No, I regret this isn't an entry on Warren Ellis's landmark sci-fi satire comic book series (I'm still figure out a way to make it apply to poi ;), the title is a great excuse to give it a plug. The planetary I'm talking about is the system by which planets rotate around a solar mass and create systems of compound elliptical orbits.