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Note 1: This 3D printed version has been superceeded by an injection molded/mass produced version which is much better and much cheaper. Go to https://superliminal.com/cube/2x2x2x2/. This version is left available for anyone with a specific reason.
Note 2: You need to buy all 8 colors to build your own puzzle
This puzzle represents the 2x2x2x2 corners of a 4D Rubik's Cube analog in a 3D embedding. It is not a simple projection into in 3D. Instead it consists of the 16 4-colored corner pieces pressed into cubes that are connected via magnets in a topology that correctly implements the 4D puzzle. All twists of two of the 8 hyperfaces are always directly available, and all the others can be reached with a gyro move.
Inspect your chains carefully. If there are any visible blemishes or uneven coloring, be sure to ask Shapeways for a reprint. I used to include 2 spare pieces per chain, but they've raised their prices too much for that, so don't hesitate to ask for a reprint if you are unhappy with any of them.
Break the pieces from the chains, arrange them with the corners up, and apply 1-to-3 coats of enamel like this. Fewer coats give a satin feel, more coats are shinier but movement is stickier.
Insert 6 magnets into each piece according to this polarity map. I recommend using needle-nose pliers with masking tape around one tip to protect the outside. Attach a magnet to the other tip, position over the hole like this and squeze gently. Take it slow and be very careful about polarity because you can't really fix any mistakes in this step. Sometimes prints will be a little too tight or loose. You can use a tiny dab of crazy glue on the end of the magnet in loose parts. Tight parts sometimes have excess plastic powder in the holes that you can scrape out and/or require a bit of force. If neither of these things work, you can ask Shapeways for a reprint of the troublesome strand.
Snap together 16 colored cubes according to the color scheme in the main photo.