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Triangular Francisco Method Guide/Algorithms

Erzz

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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.
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:
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

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

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

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

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:

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

Both Edges In D

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!
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

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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.
 

Tim Major

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

chris w

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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
 

Tim Major

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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! :p
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.
 

Erzz

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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.


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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Erzz

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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?
 

Erzz

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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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Erzz

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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.
 

Erzz

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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.

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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