Mark Longridge proposes looking for processes that can be expressed
in the form
(S1 S2 S3... SX) ^N = Goal State
He calls such a processes "Cyclicly Decomposable".
I think that the results would be far richer if there was also allowed
to be one cube rotation in the subprocess.
I know of 2 examples.
I will use a * after a move to represent a full cube move.
I am a little rusty on this one, and I don't have a cube here to verify it,
(L' R F*) ^ 6 (12q)
is (or should be, if I remember it correctly) the Pons Asinorum.
We also know that this pattern takes at best 12q, so it is actually optimum.
The existance of this process has always made me wonder how many
different ways there are to do the Pons, especially with different face
effects in the Supergroup.
The other one is my favorite process.
(L D L' R' F'*)^4 (16q)
This twists 3 corners on one face.
I suspect this one is also optimum as I have never heard of a process that
twists 3 corners in less than 16q.
It has one very interesting feature, L' R' F'* can be done as 1 combined
A casual observer may think you are only turning the cube and not see the
face turns involved. This makes the process look magic, achieving a state
in far fewer apparant moves then people think is possible.
This process is so fast and easy to remember that it is what I use while