Magnetic Rubik's Cube

Rubik's Cube comprising of 27 independent cubes, held together by magnets.
Inspired by the title text on xkcd 2049

Should be quite close to standard dimensions

You will need:
- 1 Core
- 6 Centers
- 12 Edges
- 8 Corners
- 54 Faces
- 9 each in 6 colours
- 12 disc magnets; 10mm*2mm
- 96 disc magnets; 5mm*2mm
- glue for assembly

Yes, that's a lot of magnets, but you should be able to find them on eBay easily and cheaply enough.

Highly recommended to print with supports, at high resolution

You can either print the included faces in each of the 6 colours, or just paint into the recesses where they sit.
You should also be able to print the faces either way up (45* overhangs) depending on weather you want the first or last print layer to show.
(I wonder how much of a pain it would be to use magnets to connect the faces...)

Note: I have not yet had a chance to make this myself, so I don't know if any of the tolerances I used are suitable, or if it even actually