P perms ("K perm" on the wiki):
bar on back, square on left:
R U' L U2 R' U 3r' r2 U2 r2 u2 2R2 u2 (x)
bar on back, square on right:
L' U R' U2 L U' R (l' r') U2 r2 u2 2R2 u2 (x') or maybe bar on front, square on left:
R' U L' U2 R U' 3r r2 U2 r2 u2 2R2 u2 (x')
The first one is around half a second faster than the standard Jb + opp for me. Haven't seriously drilled the second one yet, but it looks promising. There are bad regrips in both of these algs, but these are
so much shorter. Is that enough to compensate for the regrips? Sure is for me, maybe not for you, but give them a shot anyway.
Algs adapted from
the wiki page, originally credited to Clément Gallet.
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Of course you can also solve the B/D perms ("P perm" on the wiki) with variants of the above:
Da: R' U L' U2 R U' 3r
B r2 U2 r2 u2 2R2 u2 (x')
Db: R U' L U2 R' U 3r'
F r2 U2 r2 u2 2R2 u2 (x)
Ba: (r l) U2 r2 u2 2R2 u2
F 3r U' R U2 L' U R'
Bb: (r' l') U2 r2 u2 2R2 u2
B 3r' U R' U2 L U' R
Optimal for these is apparently
14 moves when restricted to u2/r2/f2, but the 14-move alg doesn't look great and is also longer in QTM. (Also, bless SiGN notation; Singmaster notation is so annoying to read.)
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Some years ago I posted this alg for X perm (it's on the wiki too):
Uw2 Rw2 U2 Rw2 R' D R' U' R (U2 D') R' D' R U2 R' (U' D) Rw2 Uw2
I no longer use this alg. The (U' D) Rw2 is too risky, and trying to keep the rarest PLL case in muscle memory when I don't even practise 444 that much seems silly. The alg I now use for this case is
the one I posted on the previous page of this thread, which is also usable on 666.
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(2020-04-30)
Another regripless X perm, this time from combining the above ideas, albeit with crappy F moves all over:
r2 U2 r2 u2 2R2 u' F' U F U' F R2 F' U F' U' F U R2 u' (21f, 29q)
You can mirror this and insert a rotation to make it RUFy, but then you'd get F2s, which might be even worse.