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BF111
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A "bandaged" 3x3x3 with more permutations than the unbandaged one.

This is a bandaged 3x3x3. In this case two opposite face cubies are connected by a massive line of spare cubies. The connector is stickered with standard stickers just for aesthetic reasons.
Between orange and red just slice moves are possible which means it is an implementation of U D L R Fs
This doesn't hinder the 3x3x3 at all. All permutations a not bandaged 3x3x3 allows are possible here too and even more. The connector makes the orientation of the red+orange faces visible so this variant has the fourfold number of permutations the not bandaged 3x3x3 has.
This anomaly would not occur if a super3x3x3 (where all face orientations are visible) had been modified like this. In this case there is just one fourth of the original permutations.

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