I've found something with LL algs

[vcuber13]

do a t perm with a dry erase marker on all the centers.

I may be wrong, but I'm fairly confident a T-perm does more than rotating one centre.

Also, I'm sure he meant to say by 90 degrees.

 

[JustinTimeCuber]

This is cool, but...
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L' (z2)
Good luck.

Spoiler: breakdown

R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
F2 F F' F F2 F F' F' F = F
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
R2 R2 R' R2 R R' R R R' = R2
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
U2 U' U U' U2 = U'
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
B2 B2 B B B = B'
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
L2 L L' L' L L L' L L' = L2
R2 B2 U2 F2 U' R2 D' L2 U B2 D L D R' U' F D R2 F' U F R F2 L' B' U2 D' L' D2 L D2 B D' B' R' D R D' R D R' D2 L D L' F D F' D' F' D' F D' L D L'
D' D D D D' D2 D2 D' D D' D D2 D D D' D' D' D = D'

wut

 

[guysensei1]

Definitely not right. How do you solve parity on a crazy fisher cube then?

So what's the conclusion about this? What happens when you get one of the leftover moves? Does it twist a center?

It's true, no center can twist 90 degrees by itself. The fisher cube can show this because it has a center with no orientation too, so you can twist that one, and one other with orientation, and it looks like you've twisted only 1 center 90 degrees.

 

[MoyuFTW]

It's true, no center can twist 90 degrees by itself. The fisher cube can show this because it has a center with no orientation too, so you can twist that one, and one other with orientation, and it looks like you've twisted only 1 center 90 degrees.

Yeah. I knew that Kind of. I know you can't twist one 90 but 180. Or you could just do the cyoubx thing and cheat.

 

[Lucas Garron]

Rule of thumb: Do any cross pieces become detached from their side colors during the alg before coming back home?

If not, then the moves on the sides *have* to cancel out: the center stayed attached to the cross edge, and the journey of cross edge canceled out.
Since many LL algs work by manipulating a few F2L pairs in clever ways, the moves will cancel for many of those.

(Technically, the aren't guaranteet won't cancel out, but the center on each site will come back. It's possible for the cross edge to travel around by a full revolution like R4, but this won't be the case for more efficient algs; they'll simply cancel out.)

U-perm is a well-known counter example. It's not supercube-safe.

 

[qqwref]

Yeah, all you really did was discover that a lot of LL algs don't orient any centers (except maybe U). There are good reasons for this. Lucas correctly points out that if the cross edges remain attached to their respective centers then the centers can't end up misoriented (except possibly the D center). It's also true that a lot of nice LL algs are made of only commutators and setup moves, and the structure of those types of algs means that.

This is not a rule, though, as there is no guarantee that a LL alg will leave the center orientations alone. Cube Explorer will happily generate LL algs that orient the centers in any possible way.

For instance, Ben found this T perm that rotates every center:
D' F2 L2 D F2 U2 F2 R2 D F2 D L2 U' F2 U2 B2 L2

 

[guysensei1]

This is not a rule, though, as there is no guarantee that a LL alg will leave the center orientations alone. Cube Explorer will happily generate LL algs that orient the centers in any possible way.

Unless you activate the center orientations