Set of 3-gen <L,U,R> PLL's!

molarmanful

Member
See here for the algorithms.

I did this just because, but there are some algorithms in there that are pretty OH-friendly.

WARNING: Some algorithms may be impractical because of length or awkwardness. These algorithms are only meant to prove that all PLL's can be 3-gen, but not that all PLL's should be 3-gen.

Of course, if you have a shorter LUR algorithm, then let me know -- I'd be happy to add it to the page.

theROUXbiksCube

Member
For Jb perm-
Antisune canceled into a Niklas

guysensei1

Member
I guess it's useful if you use ZZ and you want to <RUL> all the way.

supercavitation

Member
I use a surprising number of these for OH.

guysensei1

Member
F perm
R U R' U' R' U R U2 R' L' U R U' L U' R U' R

pdilla

Member
Huh, interesting to know.

molarmanful

Member
Okay, updated F perm.

For Rb, I decided to keep the L variation, but I acknowledge that your algorithm is faster, TDM.

G2013

Member
A shorter proof that every PLL (and even every OLL, thus every LL) is 3-gen:

J: R U R' F' R U R' U' R' F R2 U' R' U'
U counterclockwise: R2 U' R' U' R U R U R U' R

That's enough to proof that every PLL is RUF 3-gen, and: Doing F R U R' U' F' or F U R U' R' F' with some U turns you can orient all the LL edges, and doing combinations of sunes and antisunes and U turns, you can orient the corners.

The whole LL is 3-gen and I explained it in 6 lines.

A Nonconformist

Member
Umm, your Ja and Jb perms have the same result

molarmanful

Member
I like RUD better for OH than RUL
True, but RUL can always be transformed into RUD with a z rotation.

guysensei1

Member
True, but RUL can always be transformed into RUD with a z rotation.
And RUD can be turned into RUL with a z'

Why not use the standard A perm alg instead?

molarmanful

Member
And RUD can be turned into RUL with a z'

Why not use the standard A perm alg instead?
I just wanted to prove that all PLL's could be executed 3-gen RUL.

IAmAPerson

Member
Here's a collection of shorter ones.

E Perms:
R L2 U' L2 U R' U' L2 U2 L2 U' R' U L2 U' R L2
R2 L U' R2 U L' U' R2 U2 R2 U' L' U R2 U' R2 L
R2 L' U R2 U' L U R2 U2 R2 U L U' R2 U R2 L'
R' L2 U L2 U' R U L2 U2 L2 U R U' L2 U R' L2

T Perms:
U R U L' U R' U2 L U R U2 L' U2 L U' R'
U2 L U L' U R2 U' R2 U' L U' L' U R2 U R2
U2 L2 U L2 U R2 U' R2 U' L2 U' L2 U R2 U R2
U2 L2 U L2 U R' U' R U' L2 U' L2 U R' U R

Ga Perms:
U R L2 U2 R' L2 U' L U R U' L U2 R' U L2 U
U R L2 U2 L2 U' L U2 R' U R U2 L U2 R' L2 U
U R' U2 R2 U2 R2 U L U2 R2 U' R2 U R U L' U
U R' U2 R2 U2 R2 U' R2 U' R2 U2 L U' R U L' U

Gb Perms:
U2 R U' L' U R U2 L2 U' R2 U R2 L2 U2 R2 L
U2 R U' L' U R' U2 L2 U L2 U L2 U2 L2 U2 L
U2 R U' L' U' L2 U L2 U2 R' U' L2 U2 L2 U2 L
U2 R2 U' L U2 R' U L' U' R' U R2 L U2 R2 L'

Gc Perms:
U R2 L U2 R2 L2 U R2 U' L2 U2 R U L' U' R U
U R2 L' U2 R2 U R' U2 L U' L' U2 R' U2 R2 L U
U R2 L' U2 R2 L U R' U' L' U R' U2 L U' R2 U
U L U2 L2 U2 L2 U L2 U L2 U2 R' U L' U' R U

Gd Perms:
U R' L2 U2 L U2 R U R' U2 L U' L2 U2 R L2 U
U L U2 R' U' R U2 L2 U L U2 R' U' L' U2 R L
U L2 U R' U2 L U' R U L U' R' L2 U2 R L2 U
U L2 U' L U' R U2 L' U L' U2 L2 U2 R' L U2 L2

If you want any more, just ask. Also, a lot of these start with U or U'. If you want some that start with R, R', L, etc. just ask. I don't mind.

Last edited:

molarmanful

Member
Updated. Thanks SO much, IAmAPerson! Really helped!