My daughters keep bringing home various puzzle cubes, expecting me to solve them. The gear ball seems like an evil Rubik's cube. Rotating one face causes the opposing face to rotate in the opposite direction. At first my brain hurt watching it, but I now realize that the gears severely limit the number of possibilities. Here is a simple algorithm for solving it.
Let R be a clockwise rotation of the right face and U a clockwise rotation of the upper face (with an opposite rotation of the L/D face due to the gears). R' and U' are the counterclockwise rotations.
I call the [ ] shaped pieces the “edges” and the + shaped pieces the “vertices”. The square pieces in the middle are the “faces”.
We need two moves that flip certain edges and vertices (between front/back, up/down, left/right):
f/b u/d l/r ﹇ ﹇ R R U R R U' [ ] ﹈ ﹈ ﹇+ + R U R' U' R' U +﹈ +
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