The easiest way to see how the thing is put together is to take it apart.
If you turn the "top" plane 45 degrees, you can pry out the
top edge cube (any of the 4) fairly easily, and it becomes clear
how the devilish thing is put together.

In three lines or less, all the center-of-face pieces are on a
6-armed, solid, rigid cross. They can spin, but that's it.
The EDGE pieces (i.e., not the corneres) have a rectangular
projecction from their non-visible edge which gets them stuck
behind whichever two center-of-face pieces they're currently
visiting. While not rotating, it's stuck behind two. while
rotating it (a edge piece) is stuc behind the one
on its rotating face, and a groove that all edge pieces
have on their sides, in this case on the edge pieces of the
next plane back. The corner pieces have little cube-like
projections on their invisible corners that basically
wedge in behind the edge pieces, which are stuck as desribed
above. No magnets, wires, universal
joints or rubber bands.

IF youshould decide to take one apart, be SURE to put it
together SOLVED to ensure solvability.