Polaris [MI2]

Polaris is the second method that I developed. The first version was developed in January 2010. The steps were EOLine -> All 8 Corners -> UF+UB edges -> L8E. I found the UF+UB edge step too restrictive, with a high movecount. In October 2011, I found a better way of using EOLine to get to the domino reduction state and that is the method that is presented here. In August 2025, after many years of referring to the method by the codename MI2, I decided to give it a proper name - Polaris. This name aligns with the general Polar concept that I have developed in the NMLL last layer method, Polar LSLL, and the Polar ZBLL recognition method.

Original site with the CLL variant (only the main page was preserved): https://web.archive.org/web/20110224050936/http://athefre.110mb.com/

Preserved post of the main variant presented on this page: https://www.speedsolving.com/threads/random-cubing-discussion.22862/post-650817

Step 1

Solve EOLine on the left. I decided to solve EOLine in this way to avoid a z rotation for the L8E step. RUD moves weren't very easy to perform on the cubes during the year that this method was developed. However, it still felt like the right way to go. Now that we have better cubes, having the first step oriented in this way proved to be a great choice.

Step 2

Build two 1x2x3s consisting only of U/D layer oriented pieces. One 1x2x3 is on the D layer and the other one is on the U layer. The blocks can contain a mix of U/D colors. This step is extremely efficient and very easy. It takes only a few moves per block. Some of these blocks can be planned and preserved during inspection. This means proceeding to the next step is very fast. For a more advanced, even more pseudo version, the first step of the method would involve placing two U/D edges at FL and BL then build the blocks with the corners oriented toward F/B.

Step 3

Orient the remaining four corners and move the U/D edges that are on the R layer to U/D. This step is exactly the same as the first step of NMLL. Very short algs. 41 cases.

View Alg List Here

Step 4

Permute the remaining pieces. There are many ways that this can be done. A few examples:

Permute the corners then permute the edges. The edges step contains many possible substeps of its own.
- Solve two opposite edges on the D layer then permute the rest in one step.
- Make use of wide half turns or strategic slice moves while permuting the corners to simultaneously solve edges. Then permute the remaining edges in a single step.
- Solve three edges of the D layer then use L5EP.
Build any 1x1x3 bar at DL then proceed one of several ways:
- Permute the remaining six corners, solve the three remaining LR edges, then permute the M slice. In the edges step, any three edges can be solved instead of always the three remaining LR edges.
- Build a pair at bDR, permute the last five corners, then permute the last six edges.
Build any 1x2x3 block at Dl then solve the rest.

Advancements

The way forward with Polaris advancement is likely to combine corner permutation with the solving of edges. One basic idea is described below. However, this relies upon always placing correctly built pairs during Step 2. The advanced goal should be to solve Step 2 as usual with its use of any corners and edges, then permute some edges while permuting the corners.

EOLine on the D layer or L layer.
Form the two 1x2x3s consisting of blocks of pieces. The primary technique here would be to have each 1x2x3 consist of any two pairs and an edge. Other combinations are possible, however the two pair technique is a simple starting point.
Orient the remaining four corners and separate the remaining four edges. This is the same as step 3 in the original method.
Permute the pieces that were oriented in step 3 while permuting the pairs within the 1x2x3 blocks. This is the same as the permutation step of NMLL, which is only 15 cases. So for each type of pseudo 1x2x3, it would be easy to learn the corresponding algorithms.

Another idea for advancing the method is to gradually pull Step 3 further back:

Advancement 1: Solve an oriented 1x2x3 block on the bottom and an oriented 1x2x2 on the top during Step 2. Then use an alg to orient all corners while placing the FR + BR edges.
Advancement 2: Solve an oriented 1x2x3 block on the bottom then orient the remaining six corners while positioning the FR and BR edges.

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