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Encourager Cube
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A 3x3x3 that implements a subgroup but with the same number of permutations as the original.

This cube is an extension of the concept from Oskar's Enabler Cube (see the separate entry) where a specific piece of the puzzle is chosen which "enables" its shared layers to turn. Whereas the Enabler Cube uses a corner piece, the Encourager Cube has a special center piece, and it is only this center piece which can move on the puzzle. No other faces can turn independently.
The Enabler Cube implements [Dw, Rw, Bw] while the Encourager Cube implements [U, Rs, Bs]. The latter signature results in the same number of permutations as in the original cube. Since the yellow side can't be turned independently, image 7 shows a pattern that can't be achieved by just one turn.

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