Last Layer methods mapping

[MagicVince]

Hello,

As discussed in another thread, I am trying to do a mapping of the different methods to solve the Last Layer (after F2L). My sources are mainly the discussions in this forum and the wiki of this website.
Here are the results so far.
1LLL : one-look last layer. Directly solves any last layer scramble in one single algorithm.
2LLL: two-look last layer. There different methods.
- OLL + PLL (Orient Last Layer followed by Permute Last Layer). This is certainly the most known one, part of CFOP (Cross, First two layers, OLL, PLL). The recognition of the cases is probably easier than for the following methods. OLL algorithms can possibly permute the cubies while orienting them, while PLL does not affect the already solved orientations.
- CLL + ELL (Corner of Last Layer followed by Edges of Last Layer). This is probably the second best known method. CLL can have side effects on edges while adjusting the corners, whereas ELL solves the edges and leaves the corners unchanged.
- LLEF + L4C (Last Layer Edges First followed by Last Four Corners). Basically the contrary of the previous one. LLEF can disturb the corners while adjusting the edges whereas L4C solves the corners and keeps the edges unchanged.
- CPEOLL + 2GLL (Corner Permute and Edge Orient Last Layer followed by Two-Gen Last Layer). A more exotic method. The advantage is that the last step only uses 2-gen algorithms (ex. RU).
- COLL + EPLL (Corner Of Last Layer followed by Edge Permute Last Layer) is sometime considered as a 2LLL if edges orientations was fixed during F2L. COLL permute and orient corners while preserving edge orientation but can possibly permute them, since EPLL comes after and fixes edge permutation only.
3LLL and 4LLL: three-look and four-look Last Layer. Most of the two sub-phases of a 2LLL method can be decomposed into two, leading to 3LL or 4LL.
- OLL can be decomposed into EOLL + OCLL (Edge Orient Last Layer followed by Orient Corner of Last Layer).
- ELL can be decomposed into EOLL preserving corners + EPLL (Edge Orient Last Layer preserving corners followed by Edge Permute Last Layer).
- L4C can be decomposed into OCLL-EPP + CPLL (Orient Corner Last Layer Edge Preserved followed by Edge Permute Last Layer).
Some methods have a step that includes 3 actions:
- EOLL + ZBLL (Edge Orientation followed by Zborowski-Bruchem Last Layer). Once again, EOLL can be included into the F2L phase and in this case, ZBLL becomes a one-look Last Layer that solves corners while permuting edges in a single step.
- OLLCP + EPLL (Orient Last Layer and Corner Permute followed by Edge Permutation of Last Layer). OLLCP does 3 things: orient edges, orient corners and permute corners. The second step fixes what remains, that is edge permutation.

Please have a look at the following graph:

Spoiler

Questions:
- Do you spot any mistake?
- I have a doubt on OCLL-EPP: EPP should mean Edge Permutation Preserved. But L4C needs not only the permutation but also the orientation of the edges being preserved. Is it the correct naming?
- You can see in the graph several arrows with no name. Is there a standard (or at least a suggested) naming for those steps? Or are they just never used (I will remove the arrow in this case)?
- The "CPLL subset" I mentioned is only 2 algs (ex: Y-perm and T-perm) whereas CPLL is 4 algs. Is there a name for this subset (adjacent and diagonal corner swap)?
- More important: did I missed some methods?

Thanks,

Vince.

 

[Silky]

More important: did I missed some methods?

You've missed Snyder/Fish and Chips. It goes LLEF + 1 Corner -> L3C. However, this is a subset of LLEF -> L4C so it doesn't really matter. It's really just a nuance of that LL approach. No reason to add it just thought I'd mention it. Also, awesome graph Would love to see something like this for LS/LL

 

[Silky]

Oop, just two more things. (1) It would be nice to have a small table on the side with each algsets number of algorithms and average movecount ( doesn't look like there's a lot of room tho). (2) Perhaps consider putting HPLL in parentheses under ZBLL.

 

[MagicVince]

Thank you for your replies.

You've missed Snyder/Fish and Chips. It goes LLEF + 1 Corner -> L3C. However, this is a subset of LLEF -> L4C so it doesn't really matter. It's really just a nuance of that LL approach. No reason to add it just thought I'd mention it. Also, awesome graph Would love to see something like this for LS/LL

I have added LLE+1C followed by L3C, and also CLL+1 followed by L3E.

It would be nice to have a small table on the side with each algsets number of algorithms and average movecount

number of cases added, but average move-count is a bit difficult to find. Even for case count, I am missing LLE+1C. Do you know how many cases there are?

I have also added HPLL as an alternative name to ZBLL.
Other addition is OELL (EOLL preserving corner orientation).

Here is the new image :

Spoiler

Once again, any feedback is welcome.

 

[Thom S.]

I was exited for a moment that This thread got a new version.

 

[MagicVince]

I was exited for a moment that This thread got a new version.

Wow. This is a huge work indeed! Thank you for pointing out this thread.
And sorry if I disappointed you: my ambitions are more limited. I just want to make the list of the sub-phases of the main methods currently used to finish the Last Layer, once the First 2 Layers are done.
Since the names are not that obvious for me, I wanted to have them all in one document, and the illustrations are just there to make it easy to understand on which cubies they are acting.

 

[Noob's Cubes]

Has anyone memorized all of 1lll?

 

[OreKehStrah]

Has anyone memorized all of 1lll?

Yes, 1 person in Brazil going by EDMARTER on youtube.

 

[OreKehStrah]

Hello,

As discussed in another thread, I am trying to do a mapping of the different methods to solve the Last Layer (after F2L). My sources are mainly the discussions in this forum and the wiki of this website.
Here are the results so far.
1LLL : one-look last layer. Directly solves any last layer scramble in one single algorithm.
2LLL: two-look last layer. There different methods.
- OLL + PLL (Orient Last Layer followed by Permute Last Layer). This is certainly the most known one, part of CFOP (Cross, First two layers, OLL, PLL). The recognition of the cases is probably easier than for the following methods. OLL algorithms can possibly permute the cubies while orienting them, while PLL does not affect the already solved orientations.
- CLL + ELL (Corner of Last Layer followed by Edges of Last Layer). This is probably the second best known method. CLL can have side effects on edges while adjusting the corners, whereas ELL solves the edges and leaves the corners unchanged.
- LLEF + L4C (Last Layer Edges First followed by Last Four Corners). Basically the contrary of the previous one. LLEF can disturb the corners while adjusting the edges whereas L4C solves the corners and keeps the edges unchanged.
- CPEOLL + 2GLL (Corner Permute and Edge Orient Last Layer followed by Two-Gen Last Layer). A more exotic method. The advantage is that the last step only uses 2-gen algorithms (ex. RU).
- COLL + EPLL (Corner Of Last Layer followed by Edge Permute Last Layer) is sometime considered as a 2LLL if edges orientations was fixed during F2L. COLL permute and orient corners while preserving edge orientation but can possibly permute them, since EPLL comes after and fixes edge permutation only.
3LLL and 4LLL: three-look and four-look Last Layer. Most of the two sub-phases of a 2LLL method can be decomposed into two, leading to 3LL or 4LL.
- OLL can be decomposed into EOLL + OCLL (Edge Orient Last Layer followed by Orient Corner of Last Layer).
- ELL can be decomposed into EOLL preserving corners + EPLL (Edge Orient Last Layer preserving corners followed by Edge Permute Last Layer).
- L4C can be decomposed into OCLL-EPP + CPLL (Orient Corner Last Layer Edge Preserved followed by Edge Permute Last Layer).
Some methods have a step that includes 3 actions:
- EOLL + ZBLL (Edge Orientation followed by Zborowski-Bruchem Last Layer). Once again, EOLL can be included into the F2L phase and in this case, ZBLL becomes a one-look Last Layer that solves corners while permuting edges in a single step.
- OLLCP + EPLL (Orient Last Layer and Corner Permute followed by Edge Permutation of Last Layer). OLLCP does 3 things: orient edges, orient corners and permute corners. The second step fixes what remains, that is edge permutation.

Please have a look at the following graph:

Spoiler

View attachment 20619

Questions:
- Do you spot any mistake?
- I have a doubt on OCLL-EPP: EPP should mean Edge Permutation Preserved. But L4C needs not only the permutation but also the orientation of the edges being preserved. Is it the correct naming?
- You can see in the graph several arrows with no name. Is there a standard (or at least a suggested) naming for those steps? Or are they just never used (I will remove the arrow in this case)?
- The "CPLL subset" I mentioned is only 2 algs (ex: Y-perm and T-perm) whereas CPLL is 4 algs. Is there a name for this subset (adjacent and diagonal corner swap)?
- More important: did I missed some methods?

Thanks,

Vince.

Just realized there is another 2 look method being left out! CO using the shortest algs then using XLL/KLL/WLL/COALL or whatever you want to call it, where you do 1LLL when all the LL corners are oriented. There are about 140 cases.

 

[DuckubingCuber347]

Just realized there is another 2 look method being left out! CO using the shortest algs then using XLL/KLL/WLL/COALL or whatever you want to call it, where you do 1LLL when all the LL corners are oriented. There are about 140 cases.

I always found that one of the most interesting LL methods. Too bad most of it is very bad.

 

[Thom S.]

I always found that one of the most interesting LL methods. Too bad most of it is very bad.

You could theoretically learn 2 sets of CO and then leave out all the 4-Flip algs, clearing the algorithm quality of many bad cases(sets).

 

[MagicVince]

Just realized there is another 2 look method being left out! CO using the shortest algs then using XLL/KLL/WLL/COALL or whatever you want to call it, where you do 1LLL when all the LL corners are oriented.

Well, I am a bit reluctant to add it, because I have the feeling that most of the time people using this method do not begin from F2L then orient corner and then solve the remaining stuff but rather begin from Cross + 3 Pairs, then last Pair with Corner Orientation Control and then finish to solve the cube.

Same thing for LLE+1C (my understanding is that Snyder has as a previous step F2L+1Edge, not F2L). Or ZZ-Blah: I don't think people will first solve F2L then alter the corner orientation to be in Pi or H case and then use ZZ-Blah, so for me ZZ-Blah is not a method starting from F2L)

But if you say people are really using F2L then Corner Orientation, then solve remaining stuff then I will add it (this is just an extra arrow after all). I suggest to call this last step XLL.

 

[OreKehStrah]

I don’t see why not add it? I know someone who uses XLL. But let’s say I didn’t, you still have listed LLEF and CPEOLL. How many people do you suppose there are doing either of those as well. This is simply the corresponding system to EO into ZB. CO into XLL

 

[Silky]

I am missing LLE+1C. Do you know how many cases there are?

There are 155 cases but with 1 condition, at least 2 last layer edges must be oriented.

LLE+1C (my understanding is that Snyder has as a previous step F2L+1Edge, not F2L)

This is incorrect. You solve F2L, however when solving the last pair you use edge control to force at least 2 oriented last layer edges. Unlike corner control this can be done by just doing a sledge ( corner control is just WV I believe ).

 

[MagicVince]

You solve F2L, however when solving the last pair you use edge control to force at least 2 oriented last layer edges.

Yes, we are saying the same thing : this is F2L with partial Edge Orientation, not F2L. My arrow coming from F2L, I cannot use the number of cases you mentioned with your extra condition.

This is simply the corresponding system to EO into ZB. CO into XLL

Yes, you are right, indeed.

From this page, I understand that what I called XLL has 111 cases (am I wrong?).
And from this thread, I added ELLCP (even if I doubt it is actually used).
Here is the new mapping.

Spoiler

Hope it makes sense.

 

[GodCubing]

You could theoretically learn 2 sets of CO and then leave out all the 4-Flip algs, clearing the algorithm quality of many bad cases(sets).

Not to mention most of the algs would be wide move versions of their counter parts such as the sunes and pi

 

[Megaminx lover]

Yes, 1 person in Brazil going by EDMARTER on youtube.

I'm tempted to learn it now...

 

[abunickabhi]

Hello,

As discussed in another thread, I am trying to do a mapping of the different methods to solve the Last Layer (after F2L). My sources are mainly the discussions in this forum and the wiki of this website.
Here are the results so far.
1LLL : one-look last layer. Directly solves any last layer scramble in one single algorithm.
2LLL: two-look last layer. There different methods.
- OLL + PLL (Orient Last Layer followed by Permute Last Layer). This is certainly the most known one, part of CFOP (Cross, First two layers, OLL, PLL). The recognition of the cases is probably easier than for the following methods. OLL algorithms can possibly permute the cubies while orienting them, while PLL does not affect the already solved orientations.
- CLL + ELL (Corner of Last Layer followed by Edges of Last Layer). This is probably the second best known method. CLL can have side effects on edges while adjusting the corners, whereas ELL solves the edges and leaves the corners unchanged.
- LLEF + L4C (Last Layer Edges First followed by Last Four Corners). Basically the contrary of the previous one. LLEF can disturb the corners while adjusting the edges whereas L4C solves the corners and keeps the edges unchanged.
- CPEOLL + 2GLL (Corner Permute and Edge Orient Last Layer followed by Two-Gen Last Layer). A more exotic method. The advantage is that the last step only uses 2-gen algorithms (ex. RU).
- COLL + EPLL (Corner Of Last Layer followed by Edge Permute Last Layer) is sometime considered as a 2LLL if edges orientations was fixed during F2L. COLL permute and orient corners while preserving edge orientation but can possibly permute them, since EPLL comes after and fixes edge permutation only.
3LLL and 4LLL: three-look and four-look Last Layer. Most of the two sub-phases of a 2LLL method can be decomposed into two, leading to 3LL or 4LL.
- OLL can be decomposed into EOLL + OCLL (Edge Orient Last Layer followed by Orient Corner of Last Layer).
- ELL can be decomposed into EOLL preserving corners + EPLL (Edge Orient Last Layer preserving corners followed by Edge Permute Last Layer).
- L4C can be decomposed into OCLL-EPP + CPLL (Orient Corner Last Layer Edge Preserved followed by Edge Permute Last Layer).
Some methods have a step that includes 3 actions:
- EOLL + ZBLL (Edge Orientation followed by Zborowski-Bruchem Last Layer). Once again, EOLL can be included into the F2L phase and in this case, ZBLL becomes a one-look Last Layer that solves corners while permuting edges in a single step.
- OLLCP + EPLL (Orient Last Layer and Corner Permute followed by Edge Permutation of Last Layer). OLLCP does 3 things: orient edges, orient corners and permute corners. The second step fixes what remains, that is edge permutation.

Please have a look at the following graph:

Spoiler

View attachment 20619

Questions:
- Do you spot any mistake?
- I have a doubt on OCLL-EPP: EPP should mean Edge Permutation Preserved. But L4C needs not only the permutation but also the orientation of the edges being preserved. Is it the correct naming?
- You can see in the graph several arrows with no name. Is there a standard (or at least a suggested) naming for those steps? Or are they just never used (I will remove the arrow in this case)?
- The "CPLL subset" I mentioned is only 2 algs (ex: Y-perm and T-perm) whereas CPLL is 4 algs. Is there a name for this subset (adjacent and diagonal corner swap)?
- More important: did I missed some methods?

Thanks,

Vince.

Interesting connections/paths that exist. I did not know about a lot of them.

I think one more path exist, what if the person does 4C4E alg (1LLL) or two 2C2E algs instead, kinda like 2 look 1LLL. Hope that makes sense.

 

[MagicVince]

what if the person does 4C4E alg (1LLL) or two 2C2E algs instead, kinda like 2 look 1LLL.

Yes, this is interesting, I guess one could use some short algs for the first 2C2E (that disturb the rest of the LL) and other longer algs for last 2C2E (that preserve what was already done). But there are a lot of ways of choosing those 2 subsets (taking the perm notation, it could be J/J, R/R, Y/V, T/F).
This being said, I am not trying to invent a new method, just inventoring the existing ones, so unless this method is documented somewhere, I will probably drop it. But I agree that such a mapping can show where new paths could be explored.