Hi all,
The following combinations are well known on permutation puzzles, and there's some more general math behind them:
- conjugates aba'
- commutators [a, b] := aba'b'.
Consider the following:
[a, x, b] := axbx'a'xb',
and note that [a, id, b] = aba'b' = [a, b] if id is the identical operation that leaves the puzzle unchanged.
Just skimming trough the guide I was making, I can find this structure in 5 out of 8 c-OLLs:
Sune: [R, U', L']
Antisune: [L', U, R]
T: [L, F, R'] F'
Bowtie: [L, F, R'] F'
Headlights: R² [D, R', U²] R'.
--
clockwise corner-3-cycle: r' [F, R', B²] R²
I'm going to look for it in some more PLL algorithms next, but wanted to get in some feedback in the meantime.
I was wondering:
1. is there some mathematical reason for this prevalence, i.e. is it a more generally useful structure like commutators and conjugates?
2. Maybe somebody explicitly selected algorithms with this pattern for easy memorization? I can't see it highlighted in any of the guides that try to highlight patterns in their algorithms though, like the one from
badmephisto.