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Triforce: A New Unique 4x4x4 Speedsolving Method That Avoids OLL Parity

trangium

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Jul 24, 2019
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2019TRAN10
This will be a place to discuss or ask questions about the Triforce method.

Background:
Triforce is a 4x4x4 method that was developed for the August 2021 Method Development Competition.
The motivation behind Triforce's steps was to develop a method that avoids OLL parity while still being viable for speedsolving.


Steps:
1. U/D centers + 1x2x4 block (~24 moves): Solve a 1x2x4 block in dL and the first 2 centers. There are several options on how to split up this step into multiple substeps. One may choose to solve the block first, 2 centers first, center-block-center, or even freestyle.

2. Solve dM quads (~21 moves): Expand the 1x2x4 block into a 3x2x4 block while preserving the centers. After this step, R, U, and u moves will preserve the block.

3. Pair 5 U/D edges + Half Centers (~32 moves): Here, "half centers" means reducing the centers such that they can be solved with R2 and u moves. The best general approach is to get to half centers while pairing up 1-2 U/D edges, then pairing the rest of the U/D edges by setting up to u moves. Although one can't pair up E-slice edges, the fact that the centers aren't fully solved makes edge pairing more efficient overall. At some point towards the end of this step, place an E-slice edge pair in DR using an R2. This is to set up for the next step, EOLE.

4. EOLE (~7 moves, 24 algs): Use one of 24 algs to place all E-slice edges in the E slice while orienting all the U/D edges. Since one only has to recognize EO of five U/D edges, all of which are visible, recognition is extremely fast.

5. L6W (~10 moves, 14 algs): Solve the six E-slice wings. It is recommended to first solve the dFR or dBR wings, then proceed with one of 14 algs. Recognition can be tricky, but since there are so few cases, it is definitely viable.

6. L6C (~22-24 moves, 42-122 algs): Solve the 6 remaining corners without disturbing the EO or belt. The recommended approach is to first solve the 2 bottom corners (DCAL, intuitive or 80 algs), then solve the 4 top corners (CxLL, 42 algs). A y rotation should be done before starting the next step.

7. 5e5x (~19 moves): Use the m' U2 m trigger, along with U and u moves, to solve the remaining 5 edges and 5 centers simultaneously. PLL parity may happen here, but that can be fixed with (R2 u2)3 at the start of 5e5x. The key insight here is that m' U2 m cycles 3 edges and rotates the F center 180 degrees. This step can be completely intuitive but benefits from learning at least a few algs to deal with bad cases.

Pros:
  • No OLL parity, leading to an efficiency gain of ~10 moves over Yau
  • Edge pairing is less restricted
  • Good ergonomics for the majority of the solve: mostly <R, r, 3r, U, u>
Cons:
  • The 1x2x4 step can be difficult
  • A lot needs to be planned in inspection
  • A few steps have awkward movesets
  • Not that many algs will transfer from CFOP
Neutral points:
  • Many algorithmic steps, which could be a pro or a con depending on the solver
  • Many variants, which means that a solver can choose which variant they prefer, but also means that further developments could quickly render certain variants obsolete.
Additional Info:
A video tutorial by Blobinati Cuber can be found here.
More information can be found in the dedicated Triforce method doc, including example solves, FAQs, images, further details about how to do the steps, and a progression that lays out how one should start out with Triforce. Algs can be found on the Triforce method algsheet, including EOLE, L5W, DCAL, CxLL algorithms, and useful 5s5x triggers.
Join the Discord Server here.
 
Last edited:

trangium

Member
Joined
Jul 24, 2019
Messages
96
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2019TRAN10
can you do an example solve with the triforce method?
Scramble: R2 F' D2 L F' R F2 U R2 F2 L2 D2 B2 L2 D2 F D2 R2 D' Fw2 Uw2 R2 D' Rw2 F2 U B' Uw2 D2 R2 F D Rw F2 D F' Rw U D2 Fw' Rw Uw U' B2

z' // inspection
D l u f' // D center
U r' U r U2 R' u' r B2 r' // U center
F' R2 L' u U R' D' R2 U' 3r2 U' L // L block
R u2 R2 u R U u2 3r' U2 3r // B quad
u' R' u R' u R U' u 3r U2 3r' // F quad
u' R' u' R u' R2 u2 R' u R // Half centers + 1 U/D edge
u2 // 2 U/D edges
R' U' R u' // 3 U/D edges
U2 R' U' R u' R U' R u // 4 U/D edges
R' U' R' u // 5 U/D edges + EOLE setup
R s R' s' R // EOLE
u' R2 // L5W setup
x R' u R' D2 R u' R' D2 R2 x' // L5W
U R' U R' U2 R U R // DCAL
R U' L' U R' U' L // COLL
y U m' U2 m // edge reduction + 1st center
u' m' U2 m // edge reduction + 2nd center
U' u2 m' U2 m // edge reduction + 3rd center
U' 2U m' U2 m u2 // solve edges + last centers


More example solves can be found in the Triforce Method Doc that I linked in the original post, along with alg,cubing.net links. I highly recommend anyone who is interested in learning more about Triforce to check the method doc.
 

abunickabhi

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This will be a place to discuss or ask questions about the Triforce method.

Background:
Triforce is a 4x4x4 method that was developed for the August 2021 Method Development Competition.
The motivation behind Triforce's steps was to develop a method that avoids OLL parity while still being viable for speedsolving.


Steps:
1. U/D centers + 1x2x4 block (~24 moves): Solve a 1x2x4 block in dL and the first 2 centers. There are several options on how to split up this step into multiple substeps. One may choose to solve the block first, 2 centers first, center-block-center, or even freestyle.

2. Solve dM quads (~21 moves): Expand the 1x2x4 block into a 3x2x4 block while preserving the centers. After this step, R, U, and u moves will preserve the block.

3. Pair 5 U/D edges + Half Centers (~32 moves): Here, "half centers" means reducing the centers such that they can be solved with R2 and u moves. The best general approach is to get to half centers while pairing up 1-2 U/D edges, then pairing the rest of the U/D edges by setting up to u moves. Although one can't pair up E-slice edges, the fact that the centers aren't fully solved makes edge pairing more efficient overall. At some point towards the end of this step, place an E-slice edge pair in DR using an R2. This is to set up for the next step, EOLE.

4. EOLE (~7 moves, 24 algs): Use one of 24 algs to place all E-slice edges in the E slice while orienting all the U/D edges. Since one only has to recognize EO of five U/D edges, all of which are visible, recognition is extremely fast.

5. L6W (~10 moves, 14 algs): Solve the six E-slice wings. It is recommended to first solve the dFR or dBR wings, then proceed with one of 14 algs. Recognition can be tricky, but since there are so few cases, it is definitely viable.

6. L6C (~22-24 moves, 42-122 algs): Solve the 6 remaining corners without disturbing the EO or belt. The recommended approach is to first solve the 2 bottom corners (DCAL, intuitive or 80 algs), then solve the 4 top corners (CxLL, 42 algs). A y rotation should be done before starting the next step.

7. 5e5x (~19 moves): Use the m' U2 m trigger, along with U and u moves, to solve the remaining 5 edges and 5 centers simultaneously. PLL parity may happen here, but that can be fixed with (R2 u2)3 at the start of 5e5x. The key insight here is that m' U2 m cycles 3 edges and rotates the F center 180 degrees. This step can be completely intuitive but benefits from learning at least a few algs to deal with bad cases.

Pros:
  • No OLL parity, leading to an efficiency gain of ~10 moves over Yau
  • Edge pairing is less restricted
  • Good ergonomics for the majority of the solve: mostly <R, r, 3r, U, u>
Cons:
  • The 1x2x4 step can be difficult
  • A lot needs to be planned in inspection
  • A few steps have awkward movesets
  • Not that many algs will transfer from CFOP
Neutral points:
  • Many algorithmic steps, which could be a pro or a con depending on the solver
  • Many variants, which means that a solver can choose which variant they prefer, but also means that further developments could quickly render certain variants obsolete.
Additional Info:
More information can be found in the dedicated Triforce method doc, including example solves, FAQs, images, further details about how to do the steps, and a progression that lays out how one should start out with Triforce. Algs can be found on the Triforce method algsheet, including EOLE, L5W, DCAL, CxLL algorithms, and useful 5s5x triggers.
Join the Discord Server here.
Super interesting approach.

DIfferent from Yau/Hoya like methods,

and Meyer/Stadler like methods.
 

trangium

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Jul 24, 2019
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2019TRAN10
which one do you use and why?
I haven't done any 4x4x4 practice since developing Triforce. Once I get back into 4x4x4 I'll probably have both Yau sessions (because I have more experience with Yau) and Triforce sessions (because I find it fun and I want to teat it out in speedsolves as I gain more experience with Triforce.)
Is somebody making a video tutorial.
Making videos is not my thing. If someone who understands the method wants to make a video tutorial, feel free.
 
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Christopher Mowla

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This method does not avoid OLL parity anymore than Cage does (which it doesn't). You have to handle it in L5W step. (Some of the algs are 4-cycles = OLL parity. We consider pure Double Parity to be OLL Parity, don't we? Double Parity is a 4-cycle!)

What I mentioned in point #1 in this post also applies to this method.
  1. (Some stuff)

    Especially if they knew the full truth behind it (and its false promises). The worst part of Sandwich, cage, etc., is sometimes it happens that a 2-cycle of wings will appear in the last slice unintentionally. So you have to fix the parity anyway. (It's not a fool-proof avoidance approach. It just increases your chances of not getting it. But you will have to constantly "fight it off" during the solve like a fly buzzing in your ear.)

The only difference here is that an algorithm is openly listed for that (those) 2-cycle 4-cycles that can occur in that stage of the solve. (And you are given a map of all of the "possible flies that want to buzz in your ear", and how to swat each and every one of them.)

So what I can tell at first glance, the only real difference between this and Cage (regarding handling of the wing edges) is that cage aims to end with a single slice's wings unsolved, whereas this method spread those wings in random parts of the cube. (I think isolating the unsolved wings in one slice is a much simpler concept, to be honest.)

Nice try though. But avoiding OLL parity is only possible if you observe the permutation at inspection and intentionally solve the cube with an even number of inner layer slice quarter turns if the permutation of wings is even and odd if it's odd. (And even more firmly, intentionally solve the first 3 centers with an even number of inner slice quarter turns if the initial permutation of wings is even, and odd if it's odd.)
 
Last edited:

PapaSmurf

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One thing to add, it avoids OLL parity in the sense that a Uw would resolve it. I would count that as being an OLL parity avoider, if not a very neat way to deal with it.

Also, we have exactly 0 evidence to whether this would be good for elite speedsolving or not. If you have some good method analysis, go ahead and we can either chose to improve the method (which is bound to happen by people simply using it) or decide to ditch it, but that won’t happen without constructive criticism which we would welcome (I say we, I need the alg sheet to do solves still).
 
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