Assemble ten identical pieces (plus a small icosahedron) into a 5 cm diameter ball. The geometry here is very confusing, but it is based on a dissection of an icosahedron. More than 10 prototypes were made of this puzzle, because the angles have to be just right, and proper exploding depends on the friction between the pieces. The pieces need to be quite smooth for proper operation, so it is now available only in polished, white strong and flexible. The photos show how I have dyed it in 5 colors.
The small icosahedron can be replaced by a standard size D20 (~19mm face to face, the photos show a Game Science D20). This puzzle fits rather tightly out of the box, but loosens up with time.