trangium
Regular
Pinwheel LL Algs
I was inspired by the possibility of a 67 alg 2LLL (CLL+flip FR, ELL+flip FR), lower than any other standard 2LLL method. The problem is, as you might guess, the algs are really bad because of the flipped edge. But how good could a 2LLL like this be?
To beat CFCE's 71 algs, you also need a corners -> edges approach, but there have to be an odd number of bad edges in the U layer at the start of the second look. This way, you avoid any rotationally symmetric low-probability cases that drive up the second look's algcount. There are better ways to get this than flipping an edge, though. Reducing to the state F R U' R' from solved is a good candidate: it creates a single bad edge while staying close to solved. It also twists a corner, though, so you can't reduce to solved U layer corners. The trick is to reduce to a pinwheel shape: this time, the rotational symmetry of the pinwheel helps us keep the algcount low.
We actually have two choices here: reducing to a pinwheel with solved CP or diag CP. Either way, the Pinwheel CLLs would be decent, somewhere between CMLL and COLL. Reducing to solved CP might seem like the natural choice, but it turns out that the second step algs after diag CP are much better, including bangers like R U2 R' U2 R' F R2 U' R' and R U R' U' R' F R2 U R' U' R U' R'. In fact, 20 out of the 24 algs for Pinwheel ELL are derived from just these two by inverse-mirroring and adding slices. This leads to a really nice property of the Pinwheel ELL algs: literally every single one is rotationless, regripless, and starts and ends in homegrip.
Use Cases
This set is best used in a CFOP context as an option select for bad OLLs / OLLCPs. As a whole, the alg quality of Pinwheel ELL lies somewhere between adj and diag PLL, with 1-flips being slightly better on average. As a full set, OLL/PLL is still faster, but for bad OLL cases and good Pinwheel CLLs, it's often worth it to use Pinwheel instead. However, to use this set effectively, your CP recognition needs to be very fast - otherwise, the recognition pause will eat up any time you would have gained from a faster execution.
For reference, here are my averages for each subset of PLL and Pinwheel ELL:
Here is an example solve for reference.
Recognition
Pinwheel CLL has the same recognition as normal CLL.
An easy way to recognize the Pinwheel ELL cases is a sort of reverse Tv2. For 1-flips, check the flipped U-layer edge, and find its matching corner and opposite edge. For 3-flips, do the same thing with the flipped U-layer edge opposite the oriented one.
Block-based recognition for Pinwheel ELL is also very good. For 3-flips, you only need to check the U-layer, and all but two cases are distinguishable solely from matching blocks. The only two that aren't can be distinguished from their opposite U-layer blocks (e.g. red next to orange). For 1-flips, it's slightly harder, since you'll need to check one of the sides, but it can still be very fast: you'll look for matching blocks, opposite blocks, and in some cases checker patterns. Information from the flipped edge and any other U-layer edge is enough to distinguish the case.
Conclusion
This probably isn't the most efficient way to improve your times. But it's definitely one of the weirder sets I've created, and I was surprised by how good the algs were. If you learn this, you'll have a novel LL approach under your belt that you can use when the time is right, and you'll get some absolutely insane last layer solutions.
- Pinwheel CLL (43 algs) permutes the corners into a pinwheel shape with diagonal CP while doing R U R' F' to the F2L.
- Pinwheel ELL (24 algs) solves the cube from the pinwheel + R U R' F' state.
I was inspired by the possibility of a 67 alg 2LLL (CLL+flip FR, ELL+flip FR), lower than any other standard 2LLL method. The problem is, as you might guess, the algs are really bad because of the flipped edge. But how good could a 2LLL like this be?
To beat CFCE's 71 algs, you also need a corners -> edges approach, but there have to be an odd number of bad edges in the U layer at the start of the second look. This way, you avoid any rotationally symmetric low-probability cases that drive up the second look's algcount. There are better ways to get this than flipping an edge, though. Reducing to the state F R U' R' from solved is a good candidate: it creates a single bad edge while staying close to solved. It also twists a corner, though, so you can't reduce to solved U layer corners. The trick is to reduce to a pinwheel shape: this time, the rotational symmetry of the pinwheel helps us keep the algcount low.
We actually have two choices here: reducing to a pinwheel with solved CP or diag CP. Either way, the Pinwheel CLLs would be decent, somewhere between CMLL and COLL. Reducing to solved CP might seem like the natural choice, but it turns out that the second step algs after diag CP are much better, including bangers like R U2 R' U2 R' F R2 U' R' and R U R' U' R' F R2 U R' U' R U' R'. In fact, 20 out of the 24 algs for Pinwheel ELL are derived from just these two by inverse-mirroring and adding slices. This leads to a really nice property of the Pinwheel ELL algs: literally every single one is rotationless, regripless, and starts and ends in homegrip.
Use Cases
This set is best used in a CFOP context as an option select for bad OLLs / OLLCPs. As a whole, the alg quality of Pinwheel ELL lies somewhere between adj and diag PLL, with 1-flips being slightly better on average. As a full set, OLL/PLL is still faster, but for bad OLL cases and good Pinwheel CLLs, it's often worth it to use Pinwheel instead. However, to use this set effectively, your CP recognition needs to be very fast - otherwise, the recognition pause will eat up any time you would have gained from a faster execution.
For reference, here are my averages for each subset of PLL and Pinwheel ELL:
| Set / Subset | Average |
| EPLL | 0.632 |
| PLL | 0.903 |
| Adj PLL | 0.928 |
| 1-flip Pinwheel ELL | 0.970 |
| Pinwheel ELL | 1.018 |
| 3-flip Pinwheel ELL | 1.065 |
| Diag PLL | 1.075 |
Here is an example solve for reference.
Recognition
Pinwheel CLL has the same recognition as normal CLL.
An easy way to recognize the Pinwheel ELL cases is a sort of reverse Tv2. For 1-flips, check the flipped U-layer edge, and find its matching corner and opposite edge. For 3-flips, do the same thing with the flipped U-layer edge opposite the oriented one.
Block-based recognition for Pinwheel ELL is also very good. For 3-flips, you only need to check the U-layer, and all but two cases are distinguishable solely from matching blocks. The only two that aren't can be distinguished from their opposite U-layer blocks (e.g. red next to orange). For 1-flips, it's slightly harder, since you'll need to check one of the sides, but it can still be very fast: you'll look for matching blocks, opposite blocks, and in some cases checker patterns. Information from the flipped edge and any other U-layer edge is enough to distinguish the case.
Conclusion
This probably isn't the most efficient way to improve your times. But it's definitely one of the weirder sets I've created, and I was surprised by how good the algs were. If you learn this, you'll have a novel LL approach under your belt that you can use when the time is right, and you'll get some absolutely insane last layer solutions.
