I learned to solve a Rubik's cube recently by intuition and some basic cube theory (not by myself). At the last step, I use corner 3-cycles and corner rotations to reach the final solved state. I understood corner rotation this way: If a corner is rotated CW, then another corner can be rotated CCW without disturbing any other part of cube. Similarly I understood a corner 3-cycle this way (using commutator notations):
- A - replace a corner C1 from left face from right face C2. [
- B - Rotate left face so that a new corner from left face C3 gets the place where C1 was. [
- A' - place the corner C3 from where C2 was taken. [
- B' - Rotate left face the other way. [
Result: A corner 3-cycle.
I can't apply the same logic to do a 2 corner swap + 2 edge swap.
Can any one explain how J perm (or any other PLL which swaps 2 corners and 2 edges simultaneously) works?
P.S : I learned to solve the cube from this video.