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I believe the question is self-explanatory but I'm asking the question in different contexts. I understand that it makes the 3x3x3 unsolvable if you twist a single corner but there are cases where it could still be solvable if you twist pairs of corners, although I'm not sure of the mathematics behind twisting a corner of a Rubik's cube. Here are the contexts which I am particularly interested in

  • Is it a valid move in the intended original cube? Is the move "allowed" as it seems to be only available in modern constructions of the cubes

  • Is it a valid move in speedcubing? I have faced some special cases where twisting two corners would dramatically speed up solving a 2x2x2 layer

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    $\begingroup$ Do you mean twisting one corner completely by itself? (As in not rotating edges to twist the corner, but just grabbing the corner and basically snapping it into an incorrect alignment.) If that's what you mean, then no, it's not a valid move. $\endgroup$ – dcfyj Aug 11 '17 at 14:24
  • $\begingroup$ Yes, exactly "grabbing the corner and basically snapping it into an incorrect alignment" $\endgroup$ – Syafiq Kamarul Azman Aug 11 '17 at 15:21
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It's obviously not a valid move.

Many 3x3x3 speed cubes are very loose, but in my opinion the best ones are just tight enough to not allow a corner to be twisted in isolation. I don't think there are any 2x2x2 cubes that are loose enough for such a corner twist.

In an official speedcubing competition, you might find that at the end of a solve a single corner is twisted due to it popping out of alignment during the solve. In that case it is permitted to fix the problem before you stop the timer. See the WCA Regulations.

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    $\begingroup$ The regulations describe it clearly: it's only allowed if it "repairs" the puzzle, not to the competitor's advantage. Thanks for the link $\endgroup$ – Syafiq Kamarul Azman Aug 11 '17 at 15:24

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