# Superflip? How about SuperTwist?



## blgentry (May 25, 2009)

I was playing around and decided to create a condition on the cube where all edges were solved, but corners were only permuted properly, but not oriented. Using 8355 you can "solve" the cube this way, though it takes some effort to make sure all corners are un-oriented.

It's easier if you start with a solved cube though. I do it by doing a corners only OLL on the top to unorient all corners, then fix the edges that got moved with a U perm. Then I turn the cube over and do the same thing to the other side.

So, superflip has a number of algorithms that produce it, including some with great symmetry like: ((M' U)*4 x'z)*3

Do you think SuperTwist has a similar algorithm? How about it's "difficulty"? I know superflip is considered one of the more difficult cases for optimal solvers to solve. I wonder how SuperTwist rates?

Brian.


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## Ethan Rosen (May 25, 2009)

R2 B2 D B2 F2 L2 R2 D2 U' F2 R B2 F2 D2 U2 L'


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## Johannes91 (May 25, 2009)

blgentry said:


> Do you think SuperTwist has a similar algorithm?


Do you have some specific position in mind? I count 7 unique positions with edges and CP solved and all corners twisted.

Superflip is special because it's so symmetric.

Here's one supertwist alg that's similar to the superflip alg you posted:
([B R' D2 R B', U2] z)4


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## qqwref (May 25, 2009)

I converted Ethan's alg to R2 B2 [D S2 M2 U'] D2 B2 [L S2 E2 R'] but I still don't understand how it works. However the bracketed sequences are very similar so maybe that is the key.


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## blgentry (May 25, 2009)

Johannes91 said:


> Do you have some specific position in mind? There are 6 unique positions with edges and CP solved and all corners twisted.



I actually didn't realize that until I ran the previous poster's alg and saw that it was different than the one that I made "by hand". Then doing rotations between steps I realized there was a "family" of supertwist positions. I didn't know it was 7, but that sounds about right. 



> Superflip is special because it's so symmetric.



Right; only one of them and it's completely symmetric.



> Here's one supertwist alg that's similar to the superflip alg you posted:
> ([B R' D2 R B', U2] z)4



I'm either reading the alg wrong, or the alg doesn't work. Is the comma significant? I tried the alg 4 times and got a scrambled cube each time. All of the corners are twisted for sure, but they are not permuted properly and the edges are flipped and/or permuted as well.

Brian.


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## fanwuq (May 25, 2009)

blgentry said:


> > Here's one supertwist alg that's similar to the superflip alg you posted:
> > ([B R' D2 R B', U2] z)4
> 
> 
> ...



It's a commutator.

Becomes B R' D2 R B' U2 B R' D2 R B' U2
It twists 2 corners in U.

Try (R U R' U R U' R' U R U2 R' L' U' L U' L' U L U' L' U2 L z2)*2.
Double-sune from left and right.


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## qqwref (May 26, 2009)

Here are two I just found by hand:

F B U F' B' L' R' U L R
M2 U M2 U M2 U' D
L' R' U' L R F B U' F' B'
D' U M2 U' M2 U' M2 (31 stm)

R U2 R2 U' R2 U' R2 U2 R U2
F2 M B2 M'
U2 R' U2 R2 U R2 U R2 U2 R'
M B2 M' F2 (28 stm)


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## Lucas Garron (May 26, 2009)

blgentry said:


> I'm either reading the alg wrong, or the alg doesn't work. Is the comma significant?


Well, yes...
http://www.speedsolving.com/wiki/index.php/Commutators_and_Conjugates

([B R' D2 R B', U2] z)4


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## Swordsman Kirby (May 26, 2009)

qqwref said:


> Here are two I just found by hand:
> 
> F B U F' B' L' R' U L R
> M2 U M2 U M2 U' D
> ...



Both algs are great comms, but I like the second one better because of the OLL alg.


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## byu (May 26, 2009)

blgentry said:


> Johannes91 said:
> 
> 
> > Do you have some specific position in mind? There are 6 unique positions with edges and CP solved and all corners twisted.
> ...



[A, B] = A B A' B'


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## TMOY (May 26, 2009)

Another one: (L U L' U L U' L' U L U2 L' M2 S2 x2)^2


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## blgentry (May 26, 2009)

@fanwuq, Lucas, BYU: Thanks for the notation help. I didn't know that (obviously).

@fanwuq: That double Sune from both sides is exactly the kind of symmetry thing I was hoping for. Very nice! 

Brian.


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## Stefan (May 26, 2009)

Just 14 moves: U F2 L S2 U2 D2 R2 L' B2 D2 U' S2 R2 L2

Quite a few moves but easy to remember: (RU)35 z2 (RU)35

Four right+left Sunes: (R U R' U R U2 R' L' U' L U' L' U2 L z)4

And very simple: (R'Fz)140


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## blgentry (May 26, 2009)

Stephan, I don't understand how you figure out things like this. ...and seriously 140 steps?!? Wow. 

Brian.


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## brunson (May 26, 2009)

blgentry said:


> Stephan, I don't understand how you figure out things like this. ...and seriously 140 steps?!? Wow.
> 
> Brian.


That'd be 280 QTM. Got time on your hand?


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## d4m4s74 (May 26, 2009)

how bout (((U R U' R)2 D (R U R' U')2 D)2 Y2)2


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## Stefan (May 26, 2009)

blgentry said:


> Stephan, I don't understand how you figure out things like this.


I'm genius, that's all.



d4m4s74 said:


> how bout (((U R U' R)2 D (R U R' U')2 D)2 Y2)2


Even if you change the wrong R to R' so it doesn't scramble the cube anymore, this only twists four corners.

Why don't people just check their goddamn algs before they post them? Try these:
http://thearufam.brinkster.net/cube/wrapplet.asp
http://alg.garron.us/

And blgentry, these tools are the real way I figure these things out. I do *not* really repeat random moves 140 times myself. I let the program do it in an instant. Using that, it's mostly trial and error with a little bit of thinking.


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## cmhardw (May 27, 2009)

Johannes91 said:


> Do you have some specific position in mind? I count 7 unique positions with edges and CP solved and all corners twisted.



Johannes, I count more than 7.

If you ignore symmetric cases then actually I count 86 supertwist cases. I posted a long time ago about combining the superflip and the supertwist into the "super-superflip" (posted on Macky's glossary). There are 86 possible super-superflips where every piece is correctly permuted but none correctly oriented. Since the only difference between these and the supertwist is that the edges are all correctly permuted but flipped, then you should get the same number for supertwist cases ignoring symmetry.

If you do count symmetry I count the following supertwist cases:
1) 1 corner rotated clockwise, 7 rotated counter-clockwise
all these cases are symmetric to eachother (8 cases)

2) 1 corner rotated counter-clockwise, 7 rotated clockwise
all these cases are symmetric to eachother (8 cases)

All the next cases are ones with 4 corners rotated clockwise and 4 counter-clockwise. They are split into the following sub-cases based on symmetry. I list one example of each class.

1) UBR, UBL, UFL, DFR rotated clockwise, and all others rotated counter-clockwise (24 cases)

2) UBR, UBL UFL, DLF rotated clockwise, and all others rotated counter-clockwise (12 cases)

3) UBR, UBL UFL, DBR rotated clockwise, and all others rotated counter-clockwise (12 cases)

4) UBR, UFR, UBL, DBR rotated clockwise, and all others rotated counter-clockwise (8 cases)

5) UBR, UFR, DBL, DFL rotated clockwise, and all others rotated counter-clockwise (6 cases)

6) All U layer corners rotated clockwise and all D layer corners rotated counter-clockwise (6 cases)

7) UBR, UFL, DFR, DBL rotated clockwise, and all others rotated counter-clockwise (2 cases)

Giving 9 unique ways to supertwist corners, with the number of actual cases on the cube marked next to the example for each class.


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## qqwref (May 27, 2009)

I also counted 7 cases for 4 edges flipped each way, although I neglected the two cases where only one edge is flipped in one direction and 7 are flipped in the other. Good catch there.


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## Johannes91 (May 27, 2009)

The 7cw and 7ccw cases are inverses of each other and 2) and 3) are mirrors/inverses. I should've been more careful and explained what I meant by "unique", but the point was just that there's more than one.


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## blgentry (May 28, 2009)

@Stephan: Thanks for the partial explanation. I figured you were just genius.  Seriously though, many of you guys impress the hell out of me with your cube knowledge and ability.

@cmhardw: I had the same idea to do a superflip + supertwist. You obviously beat me by months or years, but it's cool that someone else thought of it. It's not exactly pretty, but it's certainly a very interesting cube state in my opinion. I wonder if you could show it to a beginner and have them understand what it means. Probably not. Oh well, it's still very cool.

Brian.


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## mrCage (Jun 3, 2009)

Hi 

A "supertwist" on corners does not really exist!! An edge 12-flip is a superflip because any conjugate of it is still the same edge 12-flip. Not so for corners. It is impossible to twist all 8 corners the same way (cw or ccw). The best "supertwist" i can think of is the position where all adjacent corners are twisted in opposite direction. This can be done very by a very short algorithm on a 2x2x2 cube ...

Another challenge would be to simply find THE shortest corner 8-twist

Per

PS! In the mid 80s i worked out a sequence for the "superfliptwist". Superflip and "supertwist" combined. My solution was 32 face turns but i dont have this with me at work of course. Oopss. I occasionally surf the cube during working hours. Gosh!!


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## Stefan (Jun 3, 2009)

mrCage said:


> A "supertwist" on corners does not really exist!!


Yes it does.



mrCage said:


> An edge 12-flip is a superflip because any conjugate of it is still the same edge 12-flip.


According to *you*.



mrCage said:


> It is impossible to twist all 8 corners the same way


So what?


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## mrCage (Jun 3, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > A "supertwist" on corners does not really exist!!
> ...


 
1. No it really does not. There is nothing "super" about a random corner 8-twist. The definition of "superness" is old as rock. I think the term was coined already back in 1981 by David Singmaster.

2. It is very easy to prove this. But again i guess you object to my terminology ...

3. Hence a "supertwist" (that is invariant by conjugation) cannot exist. The proof for this is fairly easy. If both a cw and ccw rotated corner exist, swap these 2 first by some sequence. The complete conjugated sequence gives another corner 8-twist

4. Did you solve my challenge?

Per


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## Stefan (Jun 3, 2009)

mrCage said:


> 1. The definition of "superness" is old as rock.


Show me.



mrCage said:


> 2. It is very easy to prove this.


Clarification: Of course I meant the "because".



mrCage said:


> 4. Did you solve my challenge?


I believe "THE shortest corner 8-twist" exists just as much as "THE best cube".


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## mrCage (Jun 3, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > 1. The definition of "superness" is old as rock.
> ...


 
1. I will verify this when i come home. I'm "almost 100% sure" the term superflip was coined by David Singmaster in the 1980/81 "Notes on Rubik's Magic Cube". In any case i could claim my own definition and my statement remains valid. Duh ....

4. OK fine. "A" shortest then. (you could have arrested me on metric, shortest in WHAT metric ...)


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## Stefan (Jun 3, 2009)

mrCage said:


> In any case i could claim my own definition and my statement remains valid. Duh ....


Sure. Would again be valid according to you. Neither Wikipedia, nor our wiki here, nor anyone else seems to agree on that definition.



mrCage said:


> 4. OK fine. "A" shortest then. (you could have arrested me on metric, shortest in WHAT metric ...)


Yep, the missing metric was what I meant. Might try a brute force search. There are some 14s, 16f and 20q. I guess QTM might be quickest to brute force because searches can be limited to 18q.


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## mrCage (Jun 3, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > In any case i could claim my own definition and my statement remains valid. Duh ....
> ...


 
Superflip or supertwist would be too marginal for wiki. "Cubing theory" is not a vast field judging by the number of people interested. The speedcubing community could however agree on some cube-mathematical terminology. A definition of some impossible state would not be extremely useful i guess. Nevertheless "supertwist" is an obvious counterpart to superflip (which DOES exist!)


Per


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## Stefan (Jun 3, 2009)

mrCage said:


> Superflip or supertwist would be too marginal for wiki.


http://www.speedsolving.com/wiki/index.php/Superflip
http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik's_Cube#Lower_bounds


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## mrCage (Jun 3, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > Superflip or supertwist would be too marginal for wiki.
> ...


 
OK, the term Superflip was not coined by Singmaster. But it was dicussed under another name in the before mentioned booklet. It seems Mike Reid was the one to give the 12-flip it's most common name. http://home.comcast.net/~c24m48/math/symmxm.html

Per


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## Stefan (Jun 3, 2009)

mrCage said:


> It seems Mike Reid was the one to give the 12-flip it's most common name. http://home.comcast.net/~c24m48/math/symmxm.html


And have you actually checked out his post?


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## mrCage (Jun 3, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > It seems Mike Reid was the one to give the 12-flip it's most common name. http://home.comcast.net/~c24m48/math/symmxm.html
> ...


 
Why? I have skimmed through it yes. What are you getting at ??

Per


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## Stefan (Jun 3, 2009)

mrCage said:


> StefanPochmann said:
> 
> 
> > mrCage said:
> ...



You need to improve your skimming skills. Here's the only paragraph where Mike said "superflip" in that post:



Mike Reid said:


> very nice. now how about *"superflip," and also "supertwist?"* these
> are also reasonable candidates for antipodes of "START." i know the
> following *manuever for "supertwist"* (22 face / 30 quarter turns):
> U F' U' (L R2 F2 B')^4 U F U'
> (obtained by conjugating a manuever singmaster attributes to thistlethwaite)


Not only does he mention the supertwist right next to it, and doesn't define either in a way that would make supertwist impossible like you claim, no, he even gives an example. How could you miss that?

Oh and note that Jerry writes _"Superflip (an alternate name in Singmaster is the 12-flip)"_. Plus even you yourself just wrote _"It seems Mike Reid was the one to give the 12-flip it's most common name"_. So do we agree now that superflip is just a name for the 12-flip? So that supertwist is a valid name for an 8-twist?


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## qqwref (Jun 4, 2009)

I have always assumed that the name "superflip" came from the fact that it flipped every edge (not just some random edge flip pattern, but the SUPER-flip pattern). The fact that it commutes with everything and is the same under any conjugation (and is thus part of the center of the Rubik's Cube group) are very interesting, but are NOT necessary for the name to make sense.



Mike Reid said:


> (L R2 F2 B')^4


This is an AWESOME supertwist alg.


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## mrCage (Jun 4, 2009)

StefanPochmann said:


> mrCage said:
> 
> 
> > StefanPochmann said:
> ...


 
Hmm. Empirically my odds are bad for not accepting that definition of a supertwist. But i still insist that this use of "super" breaks the spirit of its original meaning. Oh well, not a big deal really.

One can SUPERTWIST a pyraminx, im fine with that

Per


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## Stefan (Jun 4, 2009)

qqwref said:


> Mike Reid said:
> 
> 
> > (L R2 F2 B')^4
> ...


Haha, I need to improve my skimming skills as well. Didn't even notice that this middle part is a supertwist and how nice it is.

Then again, Mike's conjugation shows that he had a particular 8-twist in mind, not just any, so apparently our usage of "supertwist" does differ from the original meaning. Looks like it only referred to the one with adjacent corners twisted differently.

Also, since he didn't tell anything about the superflip and didn't clearly define the supertwist, I do get the feeling that that post was not where these terms were first introduced.


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## d4m4s74 (Jun 4, 2009)

StefanPochmann said:


> blgentry said:
> 
> 
> > Stephan, I don't understand how you figure out things like this.
> ...


with exception of the R/R' mistake it seems to work
the only mistake is that Y should have been a z or x


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## mrCage (Jun 4, 2009)

Hi 

Here is what i found for the "nearest supertwist" algorithm. Every adjacent corner twist in opposite direction.

I did not have time to let CubeExp run to completion on this one though:

U2 L2 B L2 R2 D2 U2 B2 F' R2 U L2 R2 B2 F2 D' (16f)

[U2 L2 B m2 e2 B2 F' R2 U m2 s2 D' (12s)]

Its qtm is quite poor however ... It seems possible to grasp how this one works

Per


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## rokicki (Jun 4, 2009)

16f is optimal for that position; 22q is optimal as well:

U2 R U- F- D- R- U- R- B D- F2 L F- U- B- L- F- L- D B-


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## Cameron Pearce (Aug 27, 2016)

I made an account just to share this:

(([[[R: U]: U']: D] D)2 Z2)2

It is the most pattern based alg that I could come up with (I've come up with MANY) and it seems to compact down quite nicely.


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