Greetings, dear Rubik's cube enthusiasts!
Some of the members of this forum contacted me regarding this method. At first, I was shocked, seeing that this method piqued some interest. I tried answering the questions regarding the ZZ-Orbit method and was notified that the original document was no longer accessible and there were no longer any resources on this method.
I tried to find the original documentation I made nearly 11 years ago, and shared it with some enthusiasts, and with my permission, they have posted it here.
I had to study the matter further because I had forgotten all about Rubik's cube since I am no longer solving the Rubik's cube for more than eight years.
During my studies, and reviewing this topic, I felt the urge to make a few comments.
First and foremost, I should apologize for the inappropriate behavior I have shown here. And also, the criticism regarding my lack of punctuation and proper usage of English grammar was valid. So I sincerely apologize regarding these two matters.
After that, I should apologize for the way I used to explain the method, at the time I wasn't quite good at explaining a matter and getting it through to my audience. In my original document and my further comments, There were a few miscommunications, that have led the community to misunderstand the true purpose behind the ZZ-Orbit method.
ZZ-Orbit was at its heart, an academic/educational method. I tried using it for speed solving, but the attempt was mostly directed at solving a matter that was actively talked about at the time. And a problem, already having a solution, doesn't mean it can't be further optimized or devalue any attempts at doing so. ZZ-Orbit at the time was solely an attempt at fixing the missing link.
The method was indeed developed personally for myself, and I made a failed attempt at sharing the method. There are a few points I would like to mention about this method:
1) It was generally aimed at color-neutral people. I came from a 2x2x2 background, where color neutrality is the first thing one should practice. When you are color neutral, you can find the easiest blocks, regardless of the situation. That made a huge misunderstanding about the method and I failed to address that matter properly.
2) I generally never mentioned anything about the steps leading to the formation of FDL and FDR blocks. Before switching to the ZZ method, I was using the roux method, and I had shared my modified roux method here as well. The way I usually went about solving on my own was by building two 2x2x1 blocks on BDL and BDR, doing the ZZ-Orbit method, and then fixing all the edges using one single algorithm which I was quite fast, at the time.
For the sake of turning it into a purely ZZ variation, I made a few changes.
It is worth mentioning that the newly developed EOcross method doesn't change anything. Simply make the EOcross, add the BDL and BDR F2L pairs and you'll arrive at the same spot.
3) The document contains my old method as well as the ZZ-Orbit method. Pages 33 to the end are all explanations of the old method.
4) For each permutation case, two algorithms are provided. That's to give the user freedom of choice between multiple algorithms. Indeed both algorithms were chosen by two different speed solvers based on how easily they could perform the algorithms.
5) Recognition matters were explained poorly, I struggled a bit until I remembered how it was supposed to work. I should apologize for that.
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To simply clarify what this method was all about, you had your normal ZZ solve up until two F2L blocks are left, FDL and FDR.
ZZ-Orbit method:
Step 1) Then you make the FDL block and place it in its place. (30 algorithms, pages 10 - 19)
Step 2) Then you make the FDR block and place it in its place. (12 algorithms, 6 parity cases, pages 21 - 24)
Step 3) With the preparations made during steps 1 and 2, the cases in this step have been greatly reduced, which was an optimization at the time. you were left with 71 2-Gen algorithms, to permute and orient all the pieces of the last layer. (pages 26-32)
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I agreed to share the method once more simply because of educational purposes and I don't make any claims about its speed and its efficiency. Just trying to answer the curiosity made around this method.
I would be glad to answer any questions regarding this method.