This is an animated hypercube (a three-dimensional projection of a four-dimensional object) I was commissioned to do for a trailer for a mathematics book (I'll add a link here once the project is public).
This was a really interesting and weird project to do. I'd seen similar sorts of animated images before, so I had some idea of how to go about it. But making an object that can fold itself inside-out posed some problems.
Initially I tried putting it together using regular geometry, but the polygons would get twisted around themselves and make an ugly mess, so I had to switch to using NURBS. The tubes stay oriented with a ridiculous number of look-at constraints, and, thanks to the greater mathematical precision of NURBS, they keep their shape.
Building the rig was a fairly straightforward, if tedious, task. The needs of the rig were simple enough that I probably could have skipped using bones entirely, and just mapped everything to the Controllers directly. But this method was what I was more familiar with, and it helped me keep everything organized, both in the scene and in my head. Ultimately it worked out, and I don't think I would have saved all that much time doing it the other way.