12 copies of this shape form a sphere based on the structure of a dodecahedron. The addition of magnets on the sides means that you can assemble this object very quickly and have a nice stable shape. Furthermore you can assemble the object by putting the 12 pieces in a box and shaking the box.
This was inspired by a video on self-assembling viruses.
You will need 12 copies of the piece and 120 small cube magnets. If you print at 100% you need 2mm magnets, I found that printing at 150% scale and using 3mm magnets gave a more stable structure that self-assembled more quickly when shaken. The edges of the pentagons are not straight by design: this seems to speed up the self-assembly process.
Getting all 120 magnets in place is tedious. The magnets must alternate in polarity going around the shape. Thus on any one side, there must be a north and south pole. These must be the same order on each face (say north on the left, south on the right). As long as you can get one piece done correctly (check it thoroughly by using a bar of the remaining magnets!), there is a simple trick to complete the other 11 pieces which is to attach 10 more magnets around the finished piece, and then just push pairs of magnets into another piece. This is illustrated in the last pair of images above.
You will probably need to glue the magnets in. I found that on my printer (an ultimaker) I couldn't get the tolerance right so that all the holes were tight enough to hold the magnets: sometimes I thought I had been successful but then magnets would fall out a few days later. Superglue is fine for this process.
Based on communication with Dr. Arthur Olson, the author of the video that inspired this design, I would like note that the invention behind this design is protected under his U.S. patent 20100168439 "Self-Assembled Polyhedra," and that any commercial sale or use of this model or any model that incorporates the concepts described in the patent is prohibited without proper licensing from Dr. Olson