Some special 4-cycle. (II 3 cases)

Case 1






Case 2







Case 3

Some special 4-cycle. (I 3 cases)

Case 1 This is quite basic.








Tip( Add MR' and it can convert to a 2 swap)






Case 2.






Case 3

All the 2-2 swap general.

There are still some cases not listed but in general if you cannot us simple 2-2 swap use two 3-cycle.
If I find more easy 2-2 swap I will add to the existing post.

All the 2-2 swaps for 4x4x4 (IIIa, 5 Cases)

Case 1.






Case 2.
Use two 3-cycle.






Case 3.
Use two 3-cycle.






Case 4






Case 5

All the 2-2 swaps for 4x4x4 (IId,2 Cases)

Case 1






Case 2
Two 3-cycle

All the 2-2 swaps for 4x4x4 (IIc,2 Cases)

Case 1







Case 2

All the 2-2 swaps for 4x4x4 (IIb,4 Cases)

Case 1.






Case 2.






Case 3.






Case 4

All the 2-2 swaps for 4x4x4 (IIa,5 Cases)

Case 1.
Convert to Case Ic.







Case 2.






Case 3







Case 4






Case 5.

All the 2-2 swaps for 4x4x4 (Ic, 1 case)

Case 1.






Another solution.

All the 2-2 swaps for 4x4x4 (Ib, 4 cases)

Case 1.






Two 3-cycle






Case 2.






Two 3-cycle






Case 3.






Case 4

All the 2-2 swaps for 4x4x4 (Ia, 5 cases)

Case 1. (This can be used to flip two edges for 3x3x3 blind solving.







Case 2.






Use two 2-cycle. (shorter)






Case 3






Use two 3-cycle (shorter)






Case 4 (convert to case 1)






Case 5






Two 3-cycle

All the three-cycle. (III, 1 case)

There is only one case in this family.

All the three-cycle. (II, 3 cases)

Case 1.
Solution 1





Solution 2.






Case 2.
Solution 1.






Solution 2.






Case 3

All the three-cycle. (I, 4 cases)

Case 1.






Case 2.






Case 3.






Case 4. This is similar to Case3.






The other two cases in this family are just the mirror of case 1 and case 2.

All the two swap on 4x4x4 (7 cases)

The number of all the two swap on 4x4x4 is 7. I will list them all.(Case 1)







A better solution







Any second cube is not on the same side as the first one can use setup to use the case 1. (case 2)






(Case 3)





(Case 4)





Another handy way for case 4.





Case 5 is the mirror of case 2.





Case 6 is the mirror of case 3.





Case 7 is unique.

Basic 2-2 swaps.

On Rubik 4x4x4 last layer. Here is the Basic 2-2 swap.(Case 1)






Here is another basic 2-2 swap.(Case 2)







Slightly changed will be. ((Case 3)






I will make more complete list after all the 3 cycles are listed.