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All elements of the Rubik's cube group may be generated using turns of only five of the six faces, say all but the Up face. This suggests a puzzle variant: a cube with the Up center cubie glued fast. Has any work been done on such a puzzle? I played with this a bit today. Here's an U turn macro using no U turns:

B D' F L' F' B D F' R B' L F' D F B' L' F