2-Gen OLL/PLL Algs

[CubeLord]

I need to improve my LL times. Can someone please give me any 2 gen algs or direct me to anything which has some of them(already checked the wiki)????

 

[Kirjava]

only EPLL and OCLL are 2gen.

 

[Joël]

OLL: M' U' M U2 M' U' M

PLL: M2 U' M U2 M' U' M2

 

[Kirjava]

Oh I guess EOLL is too.

 

[Escher]

<Wide sune, normal sune>

There's your generator. You can conjugate with M slices too if you like.

 

[Kirjava]

<Wide sune, normal sune>

lols, <Aperm,Uperm> for PLL

 

[Stefan]

What can <r,U> or <r,u> do to LL? (no time to think about it or look it up)

 

[cuBerBruce]

What can <r,U> or <r,u> do to LL? (no time to think about it or look it up)

Using GAP:

Spoiler

gap> Aperm := R*B3*R*F2*R3*B*R*F2*R2;
(3,6,8)(11,19,27)(17,25,33)
gap> Uperm := R2*U3*F*B3*R2*F3*B*U3*R2;
(2,7,5)(18,26,34)
gap> Jperm := B2*L*U*L3*B2*R*D3*R*D*R2;
(3,8)(5,7)(18,26)(19,27)(25,33)
gap> TwBD := (R3*B*D2*B3*R*U2)^2;
(1,35,9)(8,25,19)
gap> TwAD := F*TwBD*F3;
(1,35,9)(6,17,11)
gap> TwCD := R3*TwBD*R;
(1,35,9)(3,33,27)
gap> FlA := R3*U3*D*B2*U2*D2*F3;
(1,3,8,6)(2,5,18,10,34,26,7,4)(9,33,25,17)(11,35,27,19)(12,29,21,13,42,44,47,
45,37,36,28,20,23,15,39,31)(14,38,30,22)(16,40,32,24)(41,46,48,43)
gap> FlAB := FlA*U3*(FlA^-1)*U;
(5,26)(7,18)
gap> FlAC := B3*R3*FlAB*R*B;
(2,34)(7,18)
gap> FlAD := U3*FlAB*U;
(4,10)(7,18)
gap> Gpll := Group(Aperm,Uperm,Jperm,U);
<permutation group with 4 generators>
gap> Gll := Group(Aperm,Uperm,Jperm,U,TwAD,TwBD,TwCD,FlAB,FlAC,FlAD);
<permutation group with 10 generators>
gap> Gru := Group (r,u);
<permutation group with 2 generators>
gap> GrU := Group (r,U);
<permutation group with 2 generators>
gap> Size(Intersection(Gru,Gpll));
24
gap> Size(Intersection(GrU,Gpll));
48
gap> Size(Intersection(GrU,Gru,Gpll));
24
gap> Size(Gll);
62208
gap> Size(Intersection(Gru,Gll));
5184
gap> Size(Intersection(GrU,Gll));
10368
gap> Size(Intersection(GrU,Gru,Gll));
5184

Clearly, <r,U> and <r,u> can't permute just the LL corners, except for AUF. Additionally <r,u> can't solve U or U'. So the only Plls <r,U> can solve are the ones permuting edges only, that is: U, Z, and H. <r,u> can only solve the same ones except only half of the AUF cases of each. (You can do all 4 angle cases, since you can conjugate by u, u2, or u'.)

<r,U> can solve 1/6 of all LL cases, so the only ones it can't solve are any that involve permuting the corners relative to each other. Similarly for <r,u> except the corners can only be permuted as in U2 (besides being kept fixed). So all OLLs must be possible in <r,u> or <r,U>.

 

[StachuK1992]

That's awesome, Bruce!
I can't wait for aCube4 to be ready so I can get cracking on some <r,U> OLLs

As for now, though, surely there must be some way to run through an OLL list with GAP using a similar approach, then run the output through CE?


I've been more so interested in <RrMU> algs than pure <r,U>, optimizing the cases a bit.




Also!
To prove that all OLLs can be solved with <r,U> a quick "sune" and an adjacent swap should do the trick?

 

[cuBerBruce]

As for now, though, surely there must be some way to run through an OLL list with GAP using a similar approach, then run the output through CE?

I don't think incomplete/ambiguous cube positions can be "loaded" into Cube Explorer. So I think you're stuck with entering each OLL manually into the Facelet Editor. Unless you want Cube Explorer to solve all 10368 cases individually. But then, Cube Explorer doesn't appear to support wide turns either.

 

[StachuK1992]

Oh true.
I'll just go one by one when aCube supports it.

 

[cubernya]

PLL: M2 U' M U2 M' U' M2

Whoah...I probably shouldn't use this, but I have to give it a try

 

[StachuK1992]

Why shouldn't you use it?
I get about the same time as the <R,U> alg.

 

[cubersmith]

two opposite edges flipped is kind of 2 gen

R U R' U' r R' U R U' r'

 

[StachuK1992]

That's 3 gen, either RUM or rUR.


However, this is 2 gen:
R U R' D R U' R' D'
isn't it?

 

[Schmidt]

That's 3 gen, either RUM or rUR.


However, this is 2 gen:
R U R' D R U' R' D'
isn't it?

So, R U M is 3 gen., but R U D is 2 gen?? I'm confused :confused: <-- like that

 

[Cool Frog]

So, R U M is 3 gen., but R U D is 2 gen?? I'm confused :confused: <-- like that

need more M' U M U2 M' U M

 

[Hershey]

So, R U M is 3 gen., but R U D is 2 gen?? I'm confused :confused: <-- like that

Stachu was just joking. RUD is 3 gen (it uses 3 layers).

 

[tx789]

THere's LU the mirror of RU SU EU but with a rotation that MU

 

[Schmidt]

Stachu was just joking.

Oh aha ha ha. Are mods supposed to do that?? :confused: <-- again