As I earlier posted, I’ve been learning OLLs and PLLs at a moderate pace, trying to move past the inefficiencies of the Beginner’s Method. About half-way through learning A Perm, a light bulb went off: It corner cycles the same way as the penultimate Beginner’s Method algorithm of R’ F R’ B2 R F’ R’ B2 R2 — with Aa as the far less re-grippy surrogate, and Ab (its mirror) more efficient than serial application of the Beginner’s Method algorithm. (Slowly, it’s all coming together….)

I find the A Perm one of the easier cases to recognize, with its characteristic 2x2x1 block in a top-layer corner, the block having matching colors on either side. I set up by AUF‘ing the 2x2x1 block into the front-left corner, with the 2×2 block matching the middle and bottom layers (as in the diagram to the right). If the headlights (green-xx-green in the below diagrams) are in the back, you do the Aa Perm; if the headlights are to the right, you do the Ab Perm.

Note that the red (R Lw) and its mirror (Lw’ R’) are typically written as R2. I find that they’re really a combination of an R turn and an x cube orientation — and, although written as two moves, happen in one combined fell swoop. Here’s a handful of runs through both versions of the perm:

Aa was a snap for me to learn. Ab is still a little slower for me. Ab’s last clump of moves (R U’ Lw) should occur in a single R motion that picks up the U’ and rocks the cube forward for the Lw — a sort of simultaneous x’ and R with a U’ mixed in. On a properly-tensioned cube, this works flawlessly for me; on a cube that locks or is too loose, it gets messy.

Now onto N perm…yikes!?!