# My 3x3 Corner Cycles (Please Contribute!)



## riffz (Sep 9, 2010)

https://spreadsheets.google.com/pub...NkxUbWp0UGlLdXc&single=true&gid=0&output=html

This is my list of speed optimal algorithms for corners using ULB as a buffer. I'm sure there are plenty of comms I've missed that are better than the ones I have listed, so please contribute any algs that you think are faster than the ones I have listed.

The 'Alg/Comm' column breaks the algorithm down into commutator notation (except for some algs that I knew before BLD so I remember them more easily when I don't think of them as comms), and the 'Execution' column column is to hold the alg in standard notation, although I haven't finished filling it out so you'll have to do some cancellations on your own.  There is also an 'Alternate' column for algs I wasn't sure about using.

I've included my letter scheme in case anyone is interested: 

A - UBR
B - BRU
C - RUB
D - URF
E - RFU
F - FUR
G - UFL
H - FLU
I - LUF
J - DBL
K - LDB
L - BLD
M - DRB
N - BDR
O - RBD
P - DFR
R - RDF
S - FRD
T - DFL
U - LDF
V - FLD

Enjoy!


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## Stefan (Sep 9, 2010)

BRU FRD: (U' L U L2' U' L' U R2)2


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## amostay2004 (Sep 9, 2010)

Awesome list! So far I noticed one that I would prefer mine over yours:

AI - F - A perm - F'

Will scan through the whole list now. Thanks!


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## Henrik (Sep 9, 2010)

LFD RDF, VR: R'DR U2 R'D2R U2 R'DR


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## Ville Seppänen (Sep 9, 2010)

StefanPochmann said:


> BRU FRD: (U' L U L2' U' L' U R2)2



y[RUR2U'R',F2]y'



Henrik said:


> LFD RDF, VR: R'DR U2 R'D2R U2 R'DR



x' R[D2,RU'R']R' x

I'll probably take a look at the other cases later.


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## riffz (Sep 10, 2010)

amostay2004 said:


> Awesome list! So far I noticed one that I would prefer mine over yours:
> 
> AI - F - A perm - F'
> 
> Will scan through the whole list now. Thanks!



I suck at A perms, but I can do my alg in under 1.2 consistently.



Ville Seppänen said:


> StefanPochmann said:
> 
> 
> > BRU FRD: (U' L U L2' U' L' U R2)2
> ...



I like Ville's for both of these. I'm not sure why I wasn't using that alg for BRU FRD already, seeing as I knew the insertion.

EDIT: Updated sheet to include these two.

EDIT2: Fixed cycle names involving the DLF piece.


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## riffz (Sep 13, 2010)

Updates from Macky's E perm thread:

BRU UFL (BG): x'RU'R'DRU2R'D'RU'R'x

UFL BRU (GB): x'RUR'DRU2R'D'RUR'x

I'll update the spreadsheet tonight. I'm on lunch at work right now and I forgot my password for Google Docs.


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## cmhardw (Sep 13, 2010)

> DRB DLF	MT	y R' U R [R U' R', D2] R U' R' y'


L2 U' r2 U r2 U L2 U' r2 U' r2 U



> DLF DRB	TM	y R' U R [D2, R U' R'] R U' R' y'


U' r2 U r2 U L2 U' r2 U' r2 U L2

As far as I am aware this was discovered first by Daniel Beyer by studying the move optimal algorithm.

Chris


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## iRiLLL (Sep 15, 2010)

DBL BRU
z D R2 D2 R U2 R' D2 R U2 R D' z'

or
z' U L2 U2 L D2 L' U2 L D2 L U' z


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## riffz (Sep 16, 2010)

cmhardw said:


> > DRB DLF	MT	y R' U R [R U' R', D2] R U' R' y'
> 
> 
> L2 U' r2 U r2 U L2 U' r2 U' r2 U
> ...



How do you execute that without regrips?


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## cmhardw (Sep 17, 2010)

riffz said:


> How do you execute that without regrips?



(L')2 U' r2 U (r')2 U(right ring finger) (L')2 U' r2 U' (r')2 U(right ring finger)

U' r2 U (r')2 U(right ring finger) (L')2 U' r2 U' (r')2 U(right ring finger) (L')2

There is still one slight regrip in each alg before the second (L')2 for me.

Chris


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