# Triangular Francisco Method Guide/Algorithms



## Erzz (Apr 25, 2011)

*Triangular Francisco Method -- Guide*
**Beginner's Guide Here****​qqwref is the creator of the Triangular Francisco Method. You can find his guide here. I'll expand on that in this thread, with some examples.

*1) The Triangle*



The triangle is the first step, and there are two main ways to start: A 1x3 or 2x2 block. In the spoiler there is an example for each, plus a little trick to skip a step later on. Triangle on bottom. You can also check out Lars's site for some blockbuilding tricks. This site is also very useful, nearly infinite examples. Click "B2 Bomber" for the full triangle, or "1x2x2" for just the 2x2 start.


Spoiler



1x3 example:
Scramble: L' U' D' B D' B2 U' L' D2 F B R L F' B D2 L2 B2 D2 R F U2 R D2 U2
1x3: U' R U R' B' M2
Now attach an edge to the D colour and insert the 1x3: B2 F L'
And attach the final corner: l2 U R'

2x2 example:
Scramble: R B2 U B' R2 B' R F2 D' R' L' U2 D R D R' B' D B R B2 F2 L F2 U2
Two ways to do it. We can either use the 2x1 that we see, or set up a different. Let's use the one we can see first.
2x2: F' R2 D' L
Add a corner: B' U2 R'
Other corner: U B

The other way to do this scramble:
2x2: U' F' L2 U2 R2
Corner: L U' L2
Other corner: U' F
But wait! Undo that F! What if we do an E2 before the F? Try it!
This actually comes up a lot, it's quite useful. Always look for it if you notice your corner is attached to an E edge.



*2) The E Layer*


Next is the E-layer. It's pretty straight forward, qqwref gives the basics and a couple tricks on his site. Here are some more little tricks/algorithms:


Spoiler



Switch RF and RB: R2 U R2 U' R2
Switch and flip RF and RB: R' U M' U R2 U' M U' R
Flip RF and RB: R' U R2 U M' U r' R' U' R
Bring and flip DR to FR: R u' R' U' R u R'
Bring DR to FR: R' U' R U R

Elaboration on qqwref's R2 E R2:
Look up to the first 2x2 block example. Instead of inserting the first corner with B' U2 R', insert it with B' U2 E' R'. Then insert the second corner the same way. Do a y rotation. Look at the E layer. Watch what happens when you do R2 E R2. Two edges get solved! This also happens pretty often.



*3) Corner Slot + Orient*


The next step is to insert the last D layer corner while orientating the U layer corners.
You may not like these algs, I'm not the biggest <R, U> 2-gen fan. If you have any better, you can post here. These also might be useful for free-FOP.

These algorithms are to be done before ESO, since they will probably mess up edge orientation.

First off, download Statue's CLS sheet .doc here. I edited my algs into the doc. You can do the same if you like mine better. The columns will be A through D, and the rows 1 through 7. It should be easy to understand. I'll only post the ones that I changed.

CSO Algorithms
+ cases


Spoiler








A4: U' F' L2 U' L2 U' L2 U2 L2 F
A5: maybe F' L F U L2 U L' U2 L'
A7: y' U R' U R U' R U2 R U2 R'
B1: U F' U L' U L U' F
B2: U2 M' F' M U2 M' F M could be good.
B7: L F U F' L U L' U2 L'
C2: L U F L' U L U2 F' L'
C3: L D' L2 U' L U2 L D L'
C4: y' R' U R' U2 R U R' U R2
C7: L U F U' F2 R' F2 R F' L' - Keep thumb on FRU sticker until end of first F2
D1: U2 r U' r' U' r U r' - credit to qqwref
D2: U L D' L2 U L2 D L'
D4: y' R' U R U' F U R U' R F'
D6: U F' U F U' L F L'


- cases


Spoiler








A2: U' F' U2 L' U2 L F
A5: L F' L' U F' L' U' L U' F or r U' r' U F' L' U' L U' F
A6: U2 F U2 L' U L U F'
A7: y' U R U2 R U2 R' F R' F' could be fast
B1: U2 F2 U F R’ F2 R F’
B2: L' F U2 F' U2 L' U' L2
B3: U L F L' U' L F' L'
B7: L F' L' U2 F' L' U2 L F or r U' r' U2 F' L' U2 L F or end with r U
C3: y' U' R' U' R U2 R' U' R preference
C4: F R U' R' U L F' L2 U L
C7: L F' M U F2 U2 R U l2 interesting alg, might be fast
D2: U' L F L' U2 L F' L' or U' r U r' U2 r U' r'
D3: L' U2 L F L' U2 L2 F' L' or L' U2 r U r' U2 L2 F' L'
D6: y' U' F R' F' U R' U' R


O cases


Spoiler








A2: y' R' U R2 U2 R U2 R2 U' R
A3: r B U’ L U2 r’ F’ U’ L’ or L U F’ r U2 r’ F’ U’ L’
A4: L' U' L U2 F' L F L2 U' L or L d R2‘ U‘ R2 U R2‘ U‘ R2 F‘
A5: y' R U' R2 U2 R U' R2 U' R'
A7: y' F R F' R' U' R2 U2 R' U2 R or r U r’ F’ d’ L2 U2 L’ U2 L’
B1: R2 U R2 U R2 U2 R2 or y R2 U‘ R2 U‘ R2 U2 R2
B2: U' F' U L' U2 L U' F or d‘ L‘ d L‘ U2 L d‘ L
B3: U2 F U' L' U' L U2 F'
B4: y' U R' U' R U' R' F' U2 F R
B5: U2 r U r' U r U' r' -- credit to qqwref
B6: y’ R U2 R’ U2 (R’ l’) U R’ U’ (R l)
B7: F’ L’ U2’ L U2 L’ U2’ L U2 F
C1: U2 F' U L' U' L U' F or y' U2 R' D R' U' R D' R
C2: y' U R2 U R F R2 F' R' or y‘ U R2 U l D R2 D‘ l‘
C3: L D' L2 U2 L2 D L'
C4: y' U F R' U R2 U' R F'
C7: U2 F' R U' L' U M' U or U2 L F U r U‘ r‘ U‘ L‘
D1: U' L U' F2 U' F2 U L or U’ L d’ L2 U’ L2 d L’
D2: L U2 L' U' r U2 B' U2 L' or L U2 L‘ U‘ L F2 U‘ F2 L‘
D3: U2’ L U2 L’ U2’ r U L U’ (L’ r’)
D4: L U E F2 L2 U' L2 D F - could also try U2 u' instead of U E or y’ R U R’ U’ R2 U’ F R’ F’ R2
D5: y' R F2 U R' U R U2 F2 R'
D6: r’ D’ r U2 L2 U L d R d’ L


I cases


Spoiler








A2: r' U r2 U L D' L2 B2 U' - I feel this could be made better with some more r moves, but I kept messing up, so this is as far as I got.
B2: L D' L2 U L U2 L D L'
C1: R2 U2 R' U' R U' R' U2 R'
C2: L F L2 U' L U' F' L' U2 L - can also end as R' F2 R instead of L' U2 L
or try r U (r' L') U' L U' F' L' U2 L
D2: F' U L' U L U' L' U2 L U2 F could be good


Im cases:


Spoiler








A1: r U r' U (L r) U' R' U L2 l
B2: y' L2 U L2 U L' F' L2 F L' or L2 D' L' U L2 D L2 U' L'
D1: r U r' U M2 F' U2 F M2 might be good
D2: y L' U L U' L2 U2 F' L F U2 L2 or y' F R' U R' U' R U R2 U' R2 F'



If you are new to TF, just insert the corner and use an OLL to orientate the corners. For example, if you get headlights, you can use F R U R' U' F'. Use whichever OLL is your fastest for that corner case.

*4) Edge Slot + Orient*


Now we insert the last D layer edges while orientating the U layer edges.
Most ESO algorithms I have were made by hand with different combinations of M' U M, M' U2 M, etc. None of these algorithms affect corners. You can insert the DR edge. and then do the One Edge Already Solved algorithms and you will only lose a second or so. You can insert the DR edge before CSO if you find it easier.
A 1 means the edge is orientated, a 0 means it is not. The numbers go in the order of UL -> UB -> UR -> UF.

These weren't all obtained by me, some were found here.

ESO Algorithms:

One Edge Already Solved


Spoiler



Edge already in D layer but mis-orientated:
1000 M' U2 M U' M' U M
0111 M' U' M U M' U M U2 M' U' M

Edge in UF, orientated:
1111 M' U2 M
1101 (U') M' U' M U' M' U M
1001 M' U' M U2 M' U M
1011 (U') M' U2 M U' M' U' M U2 M' U M
0101 (U) M' U M U' M' U M
0001 (U2) M' U M2 F2 M' F2 or (U2) M' (U'/U) M U2 M' U2 M (with U)

Edge in UF, mis-orientated:
1100 M' U M U M' U M U2 M' U' M or (U2) M2 U M' U M U M' U M'
1110 (U) M U M U2 M' U M' or (U2) M' U' M U' M' U' M (can be Us instead of U's)
1010 (U2) M' U M U' M' U' M
1000 (U) M' U' M
0100 F2 M' U' M U F2 or M' U' M U' M' U2 M (can be Us instead of U's)
0000 (U') M' U2 M U2 M' U M



Both Edges In D


Spoiler



Both edges in correct places, both misorientated
0000 R' r' U2 M U M2 U2 M' U' L2 D M' x2
0011 R2 U' M' U2 M U M' U' M U' R2
1010 x2 M' U' M' U' M' U' M' U' x2 (or just D' instead of U', no rotations)
1111 M' U' R2 U' M2 U2 M' U' r2 U' M2

Both edges misorientated, wrong places
0000 R r U2 M U2 M' U M2 U' R2 U M'
0011 r2 U2 M U M2 U r2 U2 M or reverse: M' U2 r2 U' M2 U' M' U2 r2
1010 R2 U M' U' R2 M U' M' U2 M
1111 M' D' M' U2 M D M

DF misorientated, wrong places
0100 M' U R' r' U M' U2 M U R2
1110 R2 U M' U' R2 U' M

DR misorientated, wrong places
1000 M' U' M U2 R r U M U' R2
1110 U M' U R2 U M U' R2

Just wrong places
0000 I got 106 optimal solutions to this case... I like M' U2 M' U M U' R r U' M' U R r
1010 x2 M' U' M' U M U' M U x2 (or Ds instead of Us, no rotations)
1100 M' D M U M' U M U M' D' M I do the D and D' with my left hand, all else with my right.
1111 M2 D M U2 M' D' M2



For those of you who are new, you can either do M' U' M, M' U M, M' U2 M, U, U', etc until you get one of the two easy cases ((U) M' U' M and M' U2 M), or just insert it and do an OLL.

*5) Permutation of the Last Layer*


Just go to the PLL section of the SpeedSolving wiki (here) for the algorithms. This is the same as the last step of Fridrich.


That concludes this for now. If there are any errors please tell me.

Example solves!


Spoiler



Finishing the scrambles from before:
Scramble: L' U' D' B D' B2 U' L' D2 F B R L F' B D2 L2 B2 D2 R F U2 R D2 U2
Triangle: U' R U R' B' M2 B2 F L' l2 U R' (12 STM) - This could be shorter.
E layer: y u2 R' U' R U R u' U2 R U' R' u2 R U M' U r' (17/29)
Edge insert 1: y M' U2 M (3/32)
CSO: y' L D’ L2 U2 L2 D L’ (7/39)
ESO: U' M' U M U2 M' U' M (8/47)
PLL: E2 Ja-perm (12/59)

Scramble: R B2 U B' R2 B' R F2 D' R' L' U2 D R D R' B' D B R B2 F2 L F2 U2
Triangle: F' R2 D' L B' U2 E' R' U B (10 STM)
E layer: y R2 E R2 R U' R' u' R U' R' (10/20)
Edge insert: y' U' M' U' M (3/23)
CSO: y' (R U R' U')x2 R U R' (11/34)
ESO: M' U' M U' M' U' M U2 M' U M (11/45)
PLL: E E-perm (17/62)

New ones:
Scramble: R2 L U' B2 F L' F U' D' R U' D2 L R2 U F B' R D F' B L2 U2 B U'
Triangle: F2 D R' U' B' L (6/6)
E layer: y2 u R U' R' (4/10)
u R U R' (4/14)
u R' U' R U R (6/20)
u r U r' U' r U r' (8/28) (22/28)
CSO: u2 U r U r' U M2 F' U2 F M2 (11/39)
ESO: U M' U' M U' M' U' M (8/47)
PLL: L U' L U L U L U' L' U' L2 U' (12/59)

Scramble: L F U' R' D L2 R2 D' R' F2 B' L R' D2 L2 R D' F2 R U' L2 F U L2 B'
Triangle: F2 L' D' F' U2 R' y R' U' R (9/9)
E layer: r U r' (3/12)
u' R U R' (4/16)
u2 U' r U r' (5/21)
R2 U R2' U' R2 (5/26) (17/26)
CSO: E' y’ U’ R’ U’ R U2 R’ U’ R (9/35)
Edge insert: y M' U2 M (4/39)
ESO: d' M' U2 M U2 M' U' M (8/47)
PLL: L' U L' U' L' U' L' U L U L2 (11/58)

Scramble: B' D F2 B' L' B R2 L U2 L' D F2 U2 D' R U R' U F2 L' F2 R D R L2
Triangle: L' U2 D' F' d' R2 (6/6)
E layer: u' R U2 R' (4/10)
u' r U' r' (4/14)
u' r U' M U' R' (6/20)
u' R' U' R U R (6/26) (20/26)
CLS: E' U' R U2 R' U R U' R' U R U' R' U' R U' R' (17/43)
Edge insert: M' U2 M (3/46)
ESO: y U2 M' U' M U' M' U' M (8/54)
PLL: x' R U' R' D R U R' D' R U R' D R U' R' D' x U' (17/71)


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## Erzz (Apr 27, 2011)

Updated some of the CSO algs to have r U / r U' etc instead of L F, -D2 is really nice now. I might go through all these again to look for cases that could be r U / l U.


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## Tim Major (Apr 27, 2011)

I must admit, I haven't read the entire post thoroughly, more scanning through, but I didn't see any full example solves. Can you do some? (With 1look for each step using the algorithms, not just the ones you know).
I'm interested in the movecount for this, and how valid it is as an actual method. It was originally meant to be basically a complete joke made off a non-cuber's statement, but it seems you've put a lot of time and work into this. Also, how's the lookahead.


Spoiler



I bookmarked the page in my mind, I'll try some solves later.


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## chris w (Apr 27, 2011)

I've also been doing this method a little recently, but instead of using CSO, ive done a bit of winter variation (F2LL). After about a week or so and am around 25secs. Move count is good for the Triangle and E slice, without CSO my LL move count isnt what it could be with more algs. Look ahead is quite good i think also as the majority of inserts are RUR' or rUr'.
http://tinyurl.com/algx-U-yB2RUR-D


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## Tim Major (Apr 27, 2011)

chris w said:


> I've also been doing this method a little recently, but instead of using CSO, ive done a bit of winter variation (F2LL). After about a week or so and am around 25secs. Move count is good for the Triangle and E slice, without CSO my LL move count isnt what it could be with more algs. Look ahead is quite good i think also as the majority of inserts are RUR' or rUr'.
> http://tinyurl.com/algx-U-yB2RUR-D



Here's a full example for people, using Chris' start, and Statue's CLS sheet, with your ESO, and my U-perm! 
I wanted to use your CLS, but I couldn't understand the names, could you add pics for easier browsing? (under each sub-category, no need for every case).

Scramble: L' B' L2 U2 L' D' R2 B2 U' F2 U D B2 U2 L2 D2 B R' B2 D R D2 U R2 U

x' U' y B2 R U R' D' (6/6)
u R U' R' u' U' r U r' u' L F' L' D' (14/20)
y' U' R U2 R2 U2 R U R' U R2 U' R' (12/32)
U' M' U M (4/36)
y M' U2 M U' M' U' M U2 M' U M (11/47)
R2 U' R' U' R U R U R U' R U (12/59)

http://tinyurl.com/3ndxztk

So a bit less efficient than CFOP (and this had a lucky triangle), but, similar to L2L4, is basically just spamming algs, so a good method, with good potential.


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## irontwig (Apr 27, 2011)

Your triangles:
F' U' F U' B' F' L U R
F' R2 D' L B R B2 D' R


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## Erzz (Apr 27, 2011)

Tim Major said:


> I wanted to use your CLS, but I couldn't understand the names, could you add pics for easier browsing? (under each sub-category, no need for every case)..



Well I assume you have Statue's CLS sheet. The first "group" is the + group (corner twisted clockwise in URF). Second group is the - group (corner twisted counterclockwise in URF). Third group is the O group (corner orientated in URF). Fourth is I (in DRF). Fifth is Im (in DRF, twisted other way). Not sure how to upload pics. I'll edit in the full example solves that I did when making this guide.




irontwig said:


> Your triangles:
> F' U' F U' B' F' L U R
> F' R2 D' L B R B2 D' R


 
These are shorter ways to do the ones I did? Thanks!

EDIT: Added two example solves for now. Second one I think is faster than first, although higher move count. I'll add more later. I think look ahead is easier than Fridrich, since you only have to locate 1 piece instead of two. Though the better your look ahead, the more you can insert two pieces at the same time.

If you wait to align D, then you can skip a move in some algorithms.


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## uberCuber (Apr 27, 2011)

first scramble: B' U R U B' L
second scramble: L2 F' R' L' F L2


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## Kirjava (Apr 27, 2011)

second scramble: D' L' D B2


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## Erzz (Apr 28, 2011)

Haha, everyone's so much better at blockbuilding than me. Is there a specific way to practice?


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## Erzz (Jun 1, 2011)

Tim Major said:


> I wanted to use your CLS, but I couldn't understand the names, could you add pics for easier browsing? (under each sub-category, no need for every case).


 
I have added pictures for each CSO category.
I also updated a few ESO algs (mainly the ones that had Fs, but a couple others too)
Also added pictures and some formatting to make it easier to look at. No more wall of text. Plus a link to Lars's block building page.
Will be generating CSO algs again Sunday/Monday, and will update once I have them. I'm going to try for more r U type stuff.

Contemplating making a video tutorial to go along with it. Should I, or is this clear enough?
Any other feedback?


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## OMGitsSolved (Jun 1, 2011)

A beginners method to get me into it would help.


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## Erzz (Jun 1, 2011)

OMGitsSolved said:


> A beginners method to get me into it would help.


 
You can just insert the edges with M' U2 M or U M' U' M, and insert corners as you would with Fridrich F2L. Then do OLL -> PLL.


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## OMGitsSolved (Jun 1, 2011)

Erzz said:


> You can just insert the edges with M' U2 M or U M' U' M, and insert corners as you would with Fridrich F2L. Then do OLL -> PLL.


 Wouldn't that be really off from TF? Oh and please make a video of all the CSO and ESO cases.


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## Erzz (Jun 1, 2011)

OMGitsSolved said:


> Wouldn't that be really off from TF? Oh and please make a video of all the CSO and ESO cases.


 
ESO can be switched with CSO if you use CLS instead of CSO.
If you want it closer to TF then you can insert corner, OLL to orientate corners, insert edges, OLL to orientate edges.
I can make the ESO video tomorrow, CSO video when I generate them all.


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## OMGitsSolved (Jun 3, 2011)

Did you make the vids?


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## Erzz (Jun 3, 2011)

OMGitsSolved said:


> Did you make the vids?


 
I tried but all my camera angles that I can do on my own are terrible. I added links to Garron's site for each ESO alg. Saturday a friend is coming over, they can help me with camera angles, so it'll probably be done then.


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## Erzz (Jun 4, 2011)

Turns out that both the example solves I had up there were actually incorrect. I fixed them, and added three more. Nothing particularly special about them, just standard stuff I'd do in a speedsolve. Also all the example solves are linked to Garron's site now.


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## Erzz (Jun 8, 2011)

*Beginner Guide*

*Triangular Francisco -- Beginner's Guide*​
Decided to make a little Beginner's Guide for TF. Requires 12 algorithms, plus PLL.
Step 1), Step 2), and Step 5) are the same as the normal method.

Step 0) Definitions
Orientated means the sticker on the piece which belongs on either the top or bottom layer is pointed up or down. If this isn't true, it's misorientated.
A D layer edge is and edge that, if the cube was solved, would be in the D layer.
A correct corner is a corner that is orientated.

*Step 3) CSO*

*Step 3a) Insert the Corner*

This step is simple and intuitive, especially if you've used Fridrich F2L. There are algorithms on the wiki if you need them.

*Step 3b) Orientate the Corners*

You can use Fridrich OLL algorithms for this step if you want. Here are some algs I chose or generated. Refer to the wiki if you don't know the names. I'll use the same positions as in the wiki unless otherwise stated.


Spoiler



Sune: R U R' U R U2 R' or R U' L' U R' U' L
Antisune (correct corner in UFL): L U2 L' U' L U' L'
H: R U R' U R U' R' U R U2 R'
Pi: R U2 R2 U' R2 U' R2 U2 R
Headlights (correct corners on R): F R U R' U' F'
T: F' U' F U r U r' or r U' r' (U d) R' U2 R
Bowtie: y' R U2 R' (U' d') l' U' l



*Step 4) ESO*

*Step 4a) Insert the Edges*

This step is simple. Find a D layer edge that isn't solved. If it is in the U layer, position it over where it belongs. This should be on the front face. If the edge is orientated, insert it with M' U2 M. If the edge is misorientated, insert it with U M' U' M. If the edge is in the D layer, just bring it out with one of those algs.

Do this with both D layer edges.

*Step 4b) Orientate the Edges*

Look at the four edges in the U layer. If they are all orientated, move on to the next step. If there is a misorientated edge, bring it to the UF position. If there is also an orientated edge, put that in the UL position. This should always be possible.
If all the edges are misorientated, do M' U2 M U2 M' U M U2 M' U2 M (or any OLL 20 alg)
If UF and UR are misorientated, do M U M' U2 M U M' (or any OLL 28 alg)
If UF and UB are misorientated, do M U M' U' M U M' U M U2 M' (or any OLL 57 alg)

Now all that's left is PLL.


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## StachuK1992 (Jun 8, 2011)

Curious, what's the average move-count here? STM is preferred. 
It's a fun method.


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## Erzz (Jun 8, 2011)

StachuK1992 said:


> Curious, what's the average move-count here? STM is preferred.
> It's a fun method.


 
All the example solves I've done seem to be around 60, except that one where I used your CLS alg since there wasn't a good CSO one. I'm not done generating CSO yet, I keep generating more and changing old ones every day.
Unless there is some way to specifically find average move count, then I'd say around 60 using the tools I have.

Edit: Also, I didn't mention this earlier since I didn't want to bump the thread for it, but I generated the 1-look ESO algs for when both of the D layer edges are in the D layer but not correct.


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## Michael Womack (Sep 4, 2011)

is that just like the belt method


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## uberCuber (Sep 4, 2011)

Michael Womack said:


> is that just like the belt method


 
Lolbump, and no.


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## Erzz (Sep 5, 2011)

Michael Womack said:


> is that just like the belt method


 
It's sort of like what Fridrich would be if you started with a triangle, used keyhole F2L, used CLS, then OL5E and finish with PLL.

Oh wait, that isn't very much like Fridrich at all. Just look at one of the example solves.

Edit: Also once ACube supports wide turns I'm going to redo all the CSO cases.


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## Georgeanderre (Oct 4, 2011)

Finally got round to reading this thread and starting to learn this method, I managed to work out most of it just by trying to solve it various ways, 

after a few solves i noticed some of the ESO cases are either missing or im just being stupid and not noticing something...?
whatever the case, the list is below and the cases i believe to exist are just left blank



Spoiler



Edge already in D layer but mis-orientated:
1000 M' U2 M U' M' U M
0111 M' U' M U M' U M U2 M' U' M

Edge in UF, orientated:
1111 M' U2 M
0111 
1011 (U') M' U2 M U' M' U' M U2 M' U M
1101 (U') M' U' M U' M' U M
0001 (U2) M' (U'/U) M U2 M' U2 M
1001 M' U' M U2 M' U M
0101 (U) M' U M U' M' U M
0011 

Edge in UF, mis-orientated:
0000 (U') M' U2 M U2 M' U M
1000 (U) M' U' M
0100 M' U' M U' M' U2 M
0010 
1110 (U) M U M U2 M' U M'
0110 
1010 (U2) M' U M U' M' U' M
1100 M' U M U M' U M U2 M' U' M



I would usually just come up with my own algorithms for cases as simple as this but ive tried and they end up just like Roux mooing, which cant be bad, but its not ideal

and lastly, sorry for reopening a potentially "dead" thread


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