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In front of me, I have a z axis cube. Sometimes when I scramble and attempt solve it, I end up with one of the centre pieces being rotated by 90 degrees.

I know that in principle it is not possible that only one centre piece is rotated by 90 degrees - it is possible to rotate two centres by 90 degrees or to rotate one center by 180 degrees. My thoughts are that it has something to do with the fact that this cube has a lot of identical pieces, and thus several can be swapped invisibly.

So far, my best way of going at this is rescrambling the cube and solving it again. Then I end up with a valid solve, I would say, about half of the time. There must be a better way...

So my question is:

Is there a way to swap some of the other pieces around in order to rotate this centre piece?

I have thought of swapping three identical edges on the face of the rotated centre (algorithm), and then moving the corner pieces until they are oriented correctly (algorithm). Of course, the centre piece is effectively not rotated, so this does not work.

The way I solve the cube is using beginner LBL, with - for ease of recognising the eventual cube shape - orienting the center pieces of the second layer after solving the first layer. I know that this should not make any difference than first solving the cube and fixing the rotated centre pieces in the end. With this in mind, I have another question:

Is there anything I should look out for while solving the cube, that could prevent the centre piece from being rotated in the end?

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Is there a way to swap some of the other pieces around in order to rotate this centre piece?

Yes there is. What you need is the V-perm move sequence.

If you look at the pieces around a centre, you will see there are two edge-corner pairs that form a flat triangle (and are in the middle of two adjacent faces of the cube shape). You need to swap those two pairs, and that is what a V-perm does.

Hold it so the twisted centre is U, with the symmetrical corner at UBR (so the pieces that will be swapped are UR+URF with UB+UBL). Then do the moves:

R' U F' U2 F' R' F U' F' R F2 U' R' U2 R2

There are other move sequences that do V-perm, but this one only twists the U centre and leaves the other centres intact. If you use some other V-perm sequence then you may need to fix some centres afterwards, but it will at least have the correct parity. I used Cube Explorer to create this move sequence.

It is possible to do this with more elementary permutations. Just twist the U by a quarter turn so that the centre is solved, and then use 3-cycles and flips and twists to put everything in place. If it seems like you need to swap two pieces, then you actually have to do a 3-cycle that involves a pair of identical pieces, or a double swap.

Is there anything I should look out for while solving the cube, that could prevent the centre piece from being rotated in the end?

Not really. As you can see above, it can be fixed by only moving pieces in the last layer, so there is nothing you can do in the first two layers that could prevent it from happening. When you begin to solve the last layer, you could solve the centre first, and only then solve the edges/corners with 3-cycles only, as described above. Don't use a V-perm, T-perm, J-perm or any other permutation that does a swap of two edges and two corners, because those will twist a centre by 90 degrees.

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  • $\begingroup$ Thanks! The V-perm does the trick. On this cube it doesn't even mess up the rest of the cube, whereas when doing this on a regular cube the thing gets all messed up. I don't find it easy to remember (yet), so I will also give the 3-cycles a try. $\endgroup$ – Abby Aug 11 '18 at 9:35
  • $\begingroup$ @Abby On a regular cube it shouldn't mess things up too much. It is supposed to swap two corners and two edges in the U layer, and nothing else. You probably made a mistake somewhere, but at least it works for you on the axis cube. $\endgroup$ – Jaap Scherphuis Aug 11 '18 at 14:31
  • $\begingroup$ Haven't practised a lot with reading algorithms (most of the time have pictures with them) so it's very likely that I messed it up. $\endgroup$ – Abby Aug 11 '18 at 14:57

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