As suggested by Vaclav Krmela (who did the initial print in the photos), this should be printed at 200 microns with 50% infill. May want to go for 100 microns if possible. Also grind the parts thoroughly with sandpaper for smooth turning (or turning at all).
Here's a part count:
6 x Centre Pieces
6 x Centre Cap Pieces
12 x Edge Pieces
8 x Corner Pieces
12 x Hyperbolic Edge Pieces
12 x Hyperbolic Corner Pieces
6 x Hyperbolic Bandaged Pieces (Clockwise)
6 x Hyperbolic Bandaged Pieces (Anti-clockwise)
1 x Core
Like many 3D-printed twisty puzzles, this print requires 6 M3 screws! Screw length should be between 10-15mm. It is possible to have longer screws (as shown in the picture), but they will be protruding above the centre pieces. Fortunately there should be enough space from the centre caps to accomodate the extra length, but would still recommend not doing that. :p
This was initially designed for SLS printing and all the parts are hollow with no supports. However, the photos currently provided clearly shows that printing with FDM printers is possible. I assume that auto-generated support was printed on the inside for this. I'm still fairly new to FDM printing, so choose whatever settings is best for supports. I didn't expect this model to be downloaded this many times, so I think I will go over this puzzle again and make all the parts solid for FDM printers in the future.