Update: Instructables user burzvingion has made a beautiful red translucent dice version of this cube. Make sure you check it out!
Tons more pictures of the process can be seen in
The pre-build gallery:
The build gallery:
Step 1: Plan out polarities
Step 2: Get some cubes
I got 3 sets of 10, as I needed 27. The extra 3 helped me test things out, which saved me some big trouble. These aren't all that precise, with romboid and trapezoidal angles aplenty, but in the end, they work well, especially as they're nicely rounded.
Step 3: Get some magnets
They have a huge selection, and I settled on their D32 3/16" disc magnets, which are 3/16" tall.
I got a pack of 100, and a pack of 25. I needed 108 for the cube prototype. If I build another, I'm going to beef up 12 of the magnets - the 6 pairs that form the axles off the center cube, probably to twice the width, perhaps to the D63: