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There are a lot solutions for oriented 3x3. They rotate all center pieces. I'm trying to solve oriented 4x4 with GabbasSoft Cube Demo. Luckily blue and green centers were same orientation, so I just rotated them correctly with 3x3 algorithm. But other centers are shuffled:

enter image description here

enter image description here

Is there some algorithms to re-arrange center pieces without break edges and corners?

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You can cycle three centre pieces of the top face as follows, using small letters to denote turns of inner layers:

r' d2 r (this removes from the top face the front-right centre piece)
U (this brings a different top face centre piece to the front-right)
r' d2 r (this swaps the front-right centre piece with the previous one)
U (this brings a different top face centre piece to the front-right)
r' d2 r (this swaps the front-right centre piece with the previous one)
U2 (this brings the empty spot to the front-right)
r' d2 r (this places the last centre piece where the first one used to be)

There are much shorter methods, but this one is easy to understand and remember. You can use this to fix the black and the red centres. You can vary the turns of the top layer to change exactly which three centres you want to cycle around.

Note however that this method cannot be used to swap just two centre pieces, which is what you need on the red and yellow faces. For those you can first use the 3x3x3 methods for rotating the red and yellow centres a quarter turn. After that, each colour can be solved individually. One will have 3 wrong centres which can be solved as above, the other will need two swaps which you can do with two 3-cycles.

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Found solution with 3-pieces swap wich I use when building last 2 centers :

l' U r U' l U r' U'

For:

F1,1 > U1,1 U1,1 > F1,2 90 F1,2 > F1.1 -90

Before:

After:

enter image description here


r U' l' U r' U' l U

For:

F2.2 > U2.2 U2.2 > F1.2 90 F1.2 > F2.2 -90

Before:

enter image description here

After:

enter image description here

Where 1.1 is left top piece of center. There are some mirror and modifiactions of this algorithms. Main idea is:

  1. First piece move from F to U goes same place and unchanged.
  2. Piece from U goes to F rotated -90 or 90 and position changed by 1.
  3. And 3rd move is pushed by 2nd piece - goes from F to F of the first piece with opposite rotation of 2nd piece.

After some swaps cube is finished. I'm not sure that this is best solution, so answer is still active.

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