• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 40,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,121
WCA
2006BARL01
YouTube
Visit Channel
This is probably the briefest 2-cycle of wings you can do (in any move metric). Perhaps it could be used by beginners for a reductionish cage method (pairing up the edges and then solving centers).

Even Cubes
Rw' F' R2 F2 u' F' Rw (9, 7)

Odd Cubes
(Rw' M) F' R2 F2 u' F' (Rw M') (9, 7)

that's pretty cool.

you think you can find one that preserves F3L but can mess up anything else?

or one that preserves centers only? (I believe optimal for that is 9 moves)
 

Christopher Mowla

Premium Member
Joined
Sep 17, 2009
Messages
1,184
Location
Earth
YouTube
Visit Channel
come on... (rU2)*5 is nine moves without the last U2 that preserves centres.

no idea for LL though.
Too long to not have in a spoiler.
It's helpful to note that (r U2)5 U2 = [r: [U2, r] [r2 U2: r]]

That is,
r
U2 r U2 r'
r2 U2
(r)
U2 r2
r'

Clearly the first and last moves are outer conjugates to complete the centers, the second piece is a commutator, the parenthesized move is the quarter turn. The only not so obvious part (well not to me, but...) is the r2 U2 conjugates.

If you start out with a solved cube and do U2 r U2 r' r2 U2, you will see that when you do (r) next, the 1x(n-2) center block in face B in slice r replaces the 1x(n-2) center block in face D in slice r of the same color. In fact, that's why this 4-cycle even works at all, because with these conjugates, r2 U2, around the quarter turn, we displace only half of the center pieces. This is similar to my main method for forming 2-cycles, regardless if it's wide turn based (the Holy Grail) or single slice turn based (conventional algs) because we do a 3-cycle of three fourths of a slice and do a quarter turn to put back half of the center pieces.

The "Standard Dedge Flip" alg, or any other 2-cycle algorithm I have derived or my methods apply to can be derived this way too.

Since (r U2)5 U2 is 2-gen, the most popular dedge flip alg that can be modeled exactly like it is "Waffle's Alg" (I know that Sarah said Chester posted it before...anyway)

l U2 r' U2 r U2 l' U2
r U2
(r')
U2 r'


(Just conjugate all of that with r' U2 r2 to achieve a transformation of that alg).

The algorithm I posted previously is literally a 2-cycle of wings but with 3x3x3 distortion as well, not a 4-cycle (you probably know this, but it seems you are relating the two different cycles too closely). Proof: See the translation link to the 5x5x5.

If there is a 2-cycle algorithm of length 9 (or even less than 12) that can preserve the centers, much less everything but the LL, I certainly don't know how to approach it. I believe I have shown that I have a good understanding of (r U2)5 U2 to the extent that I linked my representation of it with my methods. Keep in mind also that (r U2)5 U2 is so brief because, by my outline, there were several move cancellations and the commutator was as brief as a commutator can be.
 
Last edited:

Kirjava

Colourful
Joined
Mar 26, 2006
Messages
6,121
WCA
2006BARL01
YouTube
Visit Channel
Do you want something instead of M' U r2 F2 r F R' F2 r U' R M or something thart solves M' U r2 F2 r F R' F2 r U' R M

They're both the same things. ;)

EDIT:
<+RobertY> x R B' R2' U2 B' R U R' B U2 R2 B R' x'
<+RobertY> F R' F R2 U R' U' F2 U' L F' L' F
<+RobertY> Colourful: there's also R' F R F' U R2 U B U' B2 R' B R'
(M' U') (R2 B2 R' U' r B2 R') (B r2' R)
 
Last edited:

teller

REAL Fingertricks!
Joined
Dec 15, 2008
Messages
1,035
Location
West Virginia
WCA
2010COAT01
YouTube
Visit Channel
OLL 47

oll47.gif


S' R U2 R2 U' R2 U' R2 U2 R S
 

teller

REAL Fingertricks!
Joined
Dec 15, 2008
Messages
1,035
Location
West Virginia
WCA
2010COAT01
YouTube
Visit Channel
there is no way that is faster than B' (R' U' R U)*2 B or mirrors or y2 R' U' (R' F R F')*2 U R

how fast can you do it?
I have not finished the grips on this yet, so I cannot say. Wanted to put it out there because it *oozes* RU potential and you know RU can really fly sometimes. The S is probably off-putting, but I hope to set that right...
 
Top