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For the case you have shown in the picture, yes, providing you hold it at the right angle with the two flipped pieces on the top layer of the cube to the right

So, I have gotten to the point where I am almost done with the 4x4 solve. But, there are 2 edges that need switching. And they aren't the front and back edge switch that I easily find algorithms for, these are diagonal edges. I looked up diagonal edge switch algorithms and immediately got one for 3x3, so, since I am using the reduction method(reducing 4x4 to equivalent 3x3), I thought I would try it and, it messed up the corners. I had one edge in the front and one edge on the left just like in the 3x3 case, but the corners got all messed up when I fixed the edges. And then, when I went back to do the corners again, I still had the diagonal edges. I did the 3x3 diagonal edge switch algorithm 3 times now and have gotten nowhere. This is the 3x3 algorithm I'm talking about:

R U R' U R U2 R' U

That switches front and left edges on a 3x3, so I figured it should work for a 4x4 with the same edges needing swapped. But, I did this algorithm 3 times and it always messes up the corners and then when I correct the corners, I still end up with 2 edges needing to be swapped diagonally. Here is a picture of my cube(which by the way uses the Japanese coloring scheme, so blue is opposite white):

Is there a way to switch diagonal edges on a 4x4 without messing the corners up?

So, I have gotten to the point where I am almost done with the 4x4 solve. But, there are 2 edges that need switching. And they aren't the front and back edge switch that I easily find algorithms for, these are diagonal edges. I looked up diagonal edge switch algorithms and immediately got one for 3x3, so, since I am using the reduction method(reducing 4x4 to equivalent 3x3), I thought I would try it and, it messed up the corners. I had one edge in the front and one edge on the left just like in the 3x3 case, but the corners got all messed up when I fixed the edges. And then, when I went back to do the corners again, I still had the diagonal edges. I did the 3x3 diagonal edge switch algorithm 3 times now and have gotten nowhere. This is the 3x3 algorithm I'm talking about:

R U R' U R U2 R' U

That switches front and left edges on a 3x3, so I figured it should work for a 4x4 with the same edges needing swapped. But, I did this algorithm 3 times and it always messes up the corners and then when I correct the corners, I still end up with 2 edges needing to be swapped diagonally. Here is a picture of my cube(which by the way uses the Japanese coloring scheme, so blue is opposite white):

View attachment 11130 Is there a way to switch diagonal edges on a 4x4 without messing the corners up?

So, I have gotten to the point where I am almost done with the 4x4 solve. But, there are 2 edges that need switching. And they aren't the front and back edge switch that I easily find algorithms for, these are diagonal edges. I looked up diagonal edge switch algorithms and immediately got one for 3x3, so, since I am using the reduction method(reducing 4x4 to equivalent 3x3), I thought I would try it and, it messed up the corners. I had one edge in the front and one edge on the left just like in the 3x3 case, but the corners got all messed up when I fixed the edges. And then, when I went back to do the corners again, I still had the diagonal edges. I did the 3x3 diagonal edge switch algorithm 3 times now and have gotten nowhere. This is the 3x3 algorithm I'm talking about:

R U R' U R U2 R' U

That switches front and left edges on a 3x3, so I figured it should work for a 4x4 with the same edges needing swapped. But, I did this algorithm 3 times and it always messes up the corners and then when I correct the corners, I still end up with 2 edges needing to be swapped diagonally. Here is a picture of my cube(which by the way uses the Japanese coloring scheme, so blue is opposite white):

View attachment 11130 Is there a way to switch diagonal edges on a 4x4 without messing the corners up?

Basically, you setup your case into the 'front to back' case, do the algorithm (r2 U2 r2 Uw2 r2 Uw2 that icarneiro gave), and then undo the setup you did. Note that you can also just apply the front to back algorithm on your case to get a 3-cycle, which you can just solve with a 3x3 U-perm. Less efficient, but more straightforward.

Is the cube in the correct colour scheme? If white and green are top and front respectively, the right face should be green. Otherwise, you’ve disassembled the cube.

That is a condition called centers in the wrong position, however it is curable. All you have to do is either swap the Blue and Green centers or the Red and Orange centers after that fix the F2L pairs and your cube it back to healthy.

If you look at a 3x3 and hold it as you have in the picture you will notice the difference.

Meyer solves the whole first block during edge pairing, while BigRoux doesn't take the colours of most of the edges into account when pairing the first three edges. This allows you to take advantage of solved or partially solved edges during first three edges.

Meyer solves the whole first block during edge pairing, while BigRoux doesn't take the colours of most of the edges into account when pairing the first three edges. This allows you to take advantage of solved or partially solved edges during first three edges.