Nifty.

Consider buying the rods. Dowel and other materials will likely be quicker and stronger than 3D printed parts. For the dodecahedral balls, I'd usually use a tolerance of 0.05 - 0.075mm for a friction fit (so 10.1 to 10.15 diameter hole for a 10mm rod), but you'll need to experiment when you start the prints. You may need something more like 0.1 - 0.2mm clearance.

While I wouldn't recommend 3D printing the rods, if the piece isn't too large, then 3D printing the panels could be very interesting, as you could incorporate all sorts of other textures, colours, etc.