How To: Commutators for Big Cubes

[dbeyer]

Firstly, are you interested in solving the big cubes blindfolded, yet have trouble seeing the commutators?
http://tinyurl.com/pft5d
This is Chris' thread, it is very useful. Not comfy with using commutators for the wing edges still? Here is my solution to solve the wings, it is very easy, fast and is a stepping stone to using full blown commutators.

What I use is called a helper buffer method. It is almost like Pochmann's 2-cycle method for the 3x3x3, however you are cycling 3 edges back and forth.
Buffer->Target->Helper This is done w/ an ABA'B' commutator
Helper->Target->Buffer This is done w/ an BAB'A' commutator

There are three special cases that we will encounter:
Starting a new cycle
Solving the helper edge
Solving the OLL Parity

Let's establish the Helper, Buffer, and Targets (notice plural, makes setups easy, sorta like w/ 2-cycling the 3x3x3 blindfolded)

Buffer-- FRu
Helper-- UFr
Targets-- the other 6 edges on the u and r slices.
FDr, DBr, BUr, LFu, BLu, RBu

The algs:
We use these two commutators
A: RU'R'; B: [u]
A: [r]; B: U'RU

let [u] = u, u2, or u' -- likewise [r] = r, r2, or r'

You alternate between ABA'B' commutators and BAB'A' commutators.
AB commutators: RU'R'u2RUR'u2; RU'R'u'RUR'u; rU'RUr'U'R'U
BA commutators: uRU'R'u'RUR'; U'RUr2U'R'Ur2 ...
--so on and so forth

You do an AB commutator to solve the first wing, then you proceed to solve the piece after that, which was cycled to the Helper's location. Use the proper setup + a BA commutator to solve that piece, you alternate back and forth.

Special Case 1:
Starting a new cycle: What happens, the Buffer is brought into the helper buffer area before the other 23 wings are solve. You must start a new cycle. Simply pick a new location and do the setup to solve that piece. The flow continues as normal, the algorithm used to start the new cycle should be the inverse of the last one used.

Special Case 2:
Solving the Helper: This is what I call integration. You want to solve the helper and the piece paired with it.

Starting with 1, every other piece is the start of a new pair. 1,2 is a pair; 3,4 is a pair; 5,6 is a pair etc.

Odd numbers are solved w/ the AB commutator, Even Numbers are solved w/ the BA commutator. The rule of thumb the pair w/ the helper: The helper is integrated and the other wing is solved in one alg, using the commutator that would solve the target wing in a normal pair.

Solve this pair: The UFr and the LBd

LBd is the second wing in the pair, so a BA commutator would be used. I would solve that pair w/ (Ll)2 u'RU'R'uRUR' (Ll)2

Solve this pair: RDb and the UFr

RDb is the first wing in the pair, so an AB commutator would be used. I would solve that pair w/ (Dd)' rU'RUr'U'R'U (Dd)

Continuing with the solve after integration:
Ok there is nothing special about this integration thing (save for it's 1 alg to solve the pair rather than 2) The net result is you solved another pair, so you continue solving the next pair as you normally would. The first wing of the pair using an AB commutator; The second wing using a BA commutator. I did not realize this until recently, that there is no other significance to integrating the helper.

Special Case 3:
Solving the Orientation Parity: How do you determine if there is a parity? The answer, the last wing is unpaired, in other words, two solve the other 22 wings (everything but the helper and buffer) you'll require an odd number of algorithms. Starting a new cycle counts as an algorithm solving a piece counts as an algorithm, integration counts as two algorithms, because the net effect is solving two pieces. Using a memorization system that pairs locations, such as Letter Pairs or a Person Action system allows you to easily determine if there is a parity or not.

So, you've solved all of the other 22 wings. Now the Helper and Buffer are all that's left to be solved. We don't have an algorithm to directly swap the UFr and FRu. However, with a simple commutator, we can simply use a well known algorithm.

r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

Can you see the setup + commutator so that you can perform that algorithm with no cube rotations?
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(Ll)'(Bb)' RU'R'uRUR'u' (Bb)(Ll)

I would like to make a disclaimer. I've shown setup moves being done with double slice turns. I feel that double slice turns are safer for avoiding lockups. Since Commutators have no affect on other piece types, a double slice turn is fine.

[dbeyer]

To Continue:
I took a look at big cubes. I was beginning to understand how to build the components of commutators. However ... the difficulty came with cycling in the correct direction. I broke it down to myself in a text file. I wrote all of my thoughts out, did some exploratory tests. Saved the file, and sent it to Chris. He checked the file, he approved of it.
Here it is:
http://dbeyer.110mb.com/centers_commutators.txt
This helped me better understand freestyling commutators across the cube.

There is the theory behind commutators and how to cycle them in the correct direction.

I solve x-centers relatively. As I am cycling, each center is solved in the first unsolved location on that face. I use my own scheme.
I label the centers
12
34
1 would include the locations Ful, Lub, Bur, Ruf, Dfl
2 would include the locations Fru, Lfu, Blu, Rbu, Drf
3 would include the locations Fld, Lbd, Brd, Rfd, Dlb
4 would include the locations Fdr, Ldf, Bdl, Rdb, Dbr

For the U face I solve them in this order
1B
23
B is my buffer. I have a simple letter scheme as well, built upon this number scheme.

The basic method that I use involves the Buffer, I try to use the Cross section of the l and f slices as a big help to make easy commutators.

I look at the other two pieces involved in the cycle. There are three things I try if the pair isn't already interchangeable.
1: Seeing that one piece is in the cross section (that is it's on the l or f slice) I do a setup to make that piece and the buffer interchangeable on the U face. That would just take a f or l turn of course.
2: Seeing that one piece is is in the cross section, I do a setup making the other piece of the pair interchangeable on the u/d slices.
3: Seeing that one piece is interchangeable with the cross section, I do a setup to move the other piece of the pair into the cross section.

If the pair is already interchangeable, but not in the cross section, I would do a setup on the U face so that I can freestyle this basic commutator.

There are two basic commutator types:
When the pieces are interchangeable on the cross section
When the pieces are interchangeable on the U face

Int-Cross Cross section ... that leaves the Buffer as the action spot
Int-U Face ... that leaves the other piece (generally on the F/B, or L/R faces) as the action spot

Int-U Face commutators are very easy to see, in my opinion.
I will show you the 4 builds where the action spot interacts with the Buffer's location first. It will be your job to explore and freestyle it across the cube.

A: r'[u]r; B: [u]
A: r[d]r'; B: [u]
A: f[d]f'; B: [u]
A: f'[u]f; B: [u]

Remember to use AB and BA commutator types!

[dbeyer]

This is a short and simple post
Here is a list of the setups to make each piece interchangeable hence, one of the six commutators can be used.

I will list the Location, the setup, and what move interchanges the target and the helper/buffer.

LFu: --; u'
BLu: --; u2
RBu: --; u
BUr: --; r'
DBr: --; r2
FDr: --; r
FLd: L2; u2
RFd: d'L2; u2
BRd: B; r'
LBd: B; r2
UBl: B'; u
FUl: l'B'; u
DFl: D2; r2
BDl: D2; r
ULf: L'; u2
RUf: f'L'; u2
DRf: D; r2
LDf: D; r
URb: bL; u'
LUb: L; u'
DLb: L; u2
RDb: D'; r

[AvGalen]

Thanks Daniel, these kinds of topics really lift the level of this forum!

Now all I have to do is finally attempt a blind 2x2x2 solve, then practise "a little" so I can do the 3x3x3 blind. "Tomorrow" I should be able to do the 4x4x4 and I will probably have a couple of hours left during the weekend to do my first 5x5x5 solves :)

Seriously, how long did it take you to learn/develop big cubes blind?

[dbeyer]

Off and on since G.wiz 2006, Chris is a real inspiration. I looked into it even sooner than that.

I took it seriously October 19th, after a long day of competition, and a great afterparty, I go to my aunt's ... and pick up the cube. I played w/ commutator type moves. And I found URb and BUr as my buffer and helper. I then applied to rotation to the UFr and FRu.

I spent most of December learning a letter pair system. I wrote the guide for theory on free style late December or early January, that really helped me understand freestyle commutators for the centers! I put big cubes blindfolded on hold, then come February I picked them up again.

I practiced for a weekend, intent on solving the 4x4x4 blindfolded. February 4th, my brother's birthday (Superbowl sunday too), I solved the 4x4x4 blindfolded for my first time. It wasn't a big deal, it was sloooow, and I knew satisfaction would only come from something fast on the 4x4x4. I competed in the last week of Ryan Heise's previous competition. I DNF the 4x4x4 solves, and I did this early in the week ... I was boreeeed ... so I picked up the 5x5x5 ... practiced and practiced the 5x5x5. My first successful solve was 46:15 on the 5x5x5, I was soooo stoked! I've now solved the 4x4x4 in as fast as 14:39. That was w/ an attrocious cube (I lubed it ... and I'm impressed!) My fastest 5x5x5 solve ... well that's confidential :)

October 19th - March 20th; 5 months, no?
I started Full solves February 1st.
Since then even I've made a bunch of changes to my 4x4x4 method, wings method, centrals, and memorization techniques.

March ... I decided to publish my stuff here ... aren't you all lucky. Forget the yahoo forums ... the only activity there is spam. I trust that this will be pinned to the How-To Secotion :) hehe

[dbeyer]

Corner Method
2-cycles: Well this is a very powerful method, problem comes when multiple pieces are disoriented, or more than additional one cycle needs to be intitated during the execution. I still use it and love it!

Stephan Pochmann describes using the Y perm Conjugated (setup) by F'

That cancels the initial F turn, and the ending F' turn. Leaving you with a very fast algorithm. I didn't like setting up for the Y perm as a beginner 3x3x3 bldist. I prefered setups to the DFL, I knew a conjugation of the J Perm (I didn't have an optimal PLL system then either)

During Summer 2006, I really disliked all the algorithms for Pochmann's method. I tried to develop something called simul block.
Basically 12 algs to learn, all 2 Corner - 2 Edge cycles. You'd setup the Edge with an M/E move connecting the target to the buffer area (forming a 1x2x2 block) make a move to setup the Corner to the DFL, only 1 move setup required for this step too. The S slice was free ... so if any S slice edge became the target I just did an S' move ... after solving the F/B faces (2 1x3x3 blocks) I'd rotate the cube making the S slice the M slice, and cycle the edges. The method didn't work out. However, I took the new algs from it.

All 7 Corners can be setup to the DFL w/ 1 face move (Assuming the buffer is URB) I knew an alg to target each face of the DFL corner.

After Rutgers 2006, I thought about learning 21 algs for corners ... because I liked 2-cycling the corners soo much. I noticed a pattern comming up on ACube ... I then tested it ...

I realized that my old alg could be interchanged w/ the Left Handed Y perm.

So ... the 4 Core Algs to my method are

DFL: L'U'LF2R'DR'D'R2F2
LDF: L'ULUL'U'LFL'U'LULF'L'
FLD: y'RU'R'U'RUR'F'RUR'U'R'FRy
UFR: LU'R'UL'U2RU'R'U2R
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F'L'ULUL'U'LFL'U'LULF'L'F
FRU'R'U'RUR'F'RUR'U'R'FRF'
F2L'U'LF2R'DR'D'R2
Recognize these?

Those are the Core algs as I said ... I've extended the method w/o learning anything else new really. Once I looked at ACube ... I was like oohh ...

Deeper Conjugation:
Crazy Y Perms
The method that I use for 3x3, 4x4, and 5x5 corners is really efficient now. I can target 10 locations with NO setups. I would consider these algs I'm about to list Deeper Conjugations: The Y perms are conjuated by an F move ... well I conjugate by [L]F and [R]F'. This leaves only the other 11 locations requiring 1 move to setup the (you can of course set them all to the DFL)
However of the remaining 11 possible targets, 8 of them can be targeted w/ a face move that is only 1 quarter turn.

The Tricky Locations: DBR, RUF, and BLU the setup is D2, F2, and L2 respectively, the other 8 locations can be setup w/ L/L',F/F',D/D'

Here are the extra six conjugations that I use along with the original two. You'll probably laugh at the simplicity of it. I'm just talking it up, because I think it's really great! Notice a pattern?

ULUL'U'LFL'U'LULF'L2
LULUL'U'LFL'U'LULF'L
L2ULUL'U'LFL'U'LULF'
L'ULUL'U'LFL'U'LULF'L' <-- Original

y'U'R'U'RUR'F'RUR'U'R'FR2y
y'RU'R'U'RUR'F'RUR'U'R'FRy <-- Original
y'R2U'R'U'RUR'F'RUR'U'R'Fy
y'R'U'R'U'RUR'F'RUR'U'R'FR'y

This leads to the next part of my solve. Handling the PLL parity. I just made an amazing breakthrough for the 4x4x4. But that's confidential.

The algorithm that Chris Hardwick gave me
(Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2

Chris orients and does three cycles, and he likes to solve the last 2 corners and two edges w/ a T perm and crazy setups if there is a parity. For the 5x5x5, I prefer to solve the Corners. Then:
1.Restore the Wings/Centrals with LU'R'UL'U2RU'R'U2R (3x3x3 parity fix)
2.I will then proceed to solve the wings (fixing the OLL parity if necessary)
3.Solve the Centrals w/ Commutators, Using the UR as a buffer. The cube will be reduced down to the UR<->Last-Edge and URB<->UFR. Now this last algorhtim will swap the Wings on the UL and UR tredge.

You must setup so that you don't disturb the
URB and UFR corners,
the U centers,
the UR tredge
or the UL wings.

LoL! That's not as bad as it sounds.

Dx edges set to the DL and do the setup S'D2S
yD edges set the the LD and do LEL'
E slice edges make sure the edge isn't on the L face, do an [e]L[E]L' or [e]L'[E]L setup

let the little e designate moving the FL, LF, BL, LB off of the L face/slice

The U layer is interesting. I visulized the setups wrong ... costing me a few 5x5x5 blindolded solves in the beginning ... so I'm going to GIVE them to you, rather than let you explore this part.


UF: FLE'L'F'
FU: FL'E2LF'
UB: B'L'ELB
BU: B'LE2L'B

so now ... that you've done the setup ... do this T perm (because I know this alg is safe for the 5 center faces)
RUR'U'R'FR2U'R'U'RUR'F'

Undo your setup
now the UL and UR wings are swapped, we know how to fix that. Rotate the Cube y or y', whichever you prefer and finish you're cube!
(Ll)2 (Ff)2 U2 l2 U2 (Ff)2 (Ll)2

I you want to start off basic: Use those setups, and 2-cycle all of the centrals.

If you are comfortable with Centrals Commutators:
Those setups just aren't optimal ... which I just realized, that it is so even for the last edge. Explore your setups that you can use treating the professor as a 3x3x3.

Consider this
Setup1:
Alg to swap the centrals
Setup2:
Parity Fix retoring the wings
Reset2:
Reset1:

[AvGalen]

Hi Daniel,

I hope you had a good time last weekend. Due to a little bug in the "official results" database you are actually listed as the winner of the 3x3x3 bf competition. (http://www.worldcubeassociation.org/...ttahoochee2007) You should thank your parents for your names.

Seriously, what happened? You solved a 4x4x4 blind and Chris did a 4x4x4 and a 5x5x5, but neither of you did a succesfull 3x3x3? You are now ranked 4th in the world (http://www.worldcubeassociation.org/...&single=Single).

My plans for the weekend changed, so I still didn't read all of the above, but I think Erik has started to.

[dbeyer]

Haha, Chris and I talked about it ... we don't really care about 3x3x3 blindfolded, I mean we are going for fast times, not accuracy.

As for my blindfolded times:

3:15 DNF Off by a 3 cycle on the edges
3:05 DNF disoriented a pair of edges

4x4x4: Execution Error, off by a 3 cycle on the centers 14:45
4x4x4: Ranked me 4th in the world '_' ... a little hard time, forgot 2 letter pairs, but was able to skip and come back to them ... I should really add that to the guide!

5x5x5: Time 44:45ish I didn't undo a setup on the f slice, that was the only Error, there was a net turn of f2, I then continued to solve the Lfe and Rfe

Because of the net turn of f2, I permuted the f slice pieces, but not the four edges that were already there

An example, I had LP, DM ...

Put to roman rooms and images

This guy sits drunk at the barstool listening to a Linkin Park Concert
The Dungeon Master (DnD) rolls the dice and sends Jesus to the cross (the location is a porceline cross on the wall)

L was permuted, P was permuted (however D wasn't, because D came after a piece on the f slice)
M was permuted ...

the wings in the P and S locations were swapped,

I think the letter pair using S was SW, SWAT team

So when I was permuting D, I actually placed the W wing into the D location.

Considering I drove 12 hours of the 15 hour long trip, and went straight into the school and started competing, w/ 1.5 hours sleep ... I did alright!

[pjk]

Nice guide, I will put this into How-To soon. I want to start getting into bigger cubes BLD, but want to get better at 3x3 speedsolve and 3x3 BLD, along with 4x4 and 5x5 speedsolve. But within a year I will start ;)

Thanks for writing this up, it will certainly help me.

[cmhardw]

Seriously, what happened? You solved a 4x4x4 blind and Chris did a 4x4x4 and a 5x5x5, but neither of you did a succesfull 3x3x3?

Hey AvGalen, yeah Daniel and I talked about this a bunch in Georgia. I think the reason I still DNF the 3x3 under pressure is I don't have a memory system for it, only for the bigger cubes. Daniel and I talked a lot about potential memory systems for the 3x3x3, so we're working on it. Still that's my reason *cough* excuse *cough* ;-) for having DNF'd my 3x3x3 BLD solves.

Chris