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?