My 3x3 Corner Cycles (Please Contribute!)

[riffz]

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!

 

[Stefan]

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

 

[amostay2004]

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!

 

[Henrik]

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

 

[Ville Seppänen]

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

y[RUR2U'R',F2]y'

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.

 

[riffz]

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.

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

y[RUR2U'R',F2]y'

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.

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.

 

[riffz]

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.

 

[cmhardw]

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

 

[iRiLLL]

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

 

[riffz]

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

How do you execute that without regrips?

 

[cmhardw]

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