5-cycles for corner

I just finish a tutorial in french about 5-cycles corner resolution.

This method allow to solve the corners using 4 algs max.

You'll find the alg in the French tutorial, but I will explain quickly the method in English here.

First you need to orient the corner like in 3-cycle method. You can do it in 2 alg. Firstly you orient the alg of the top layer, plus, if you need, a corner of the botom layer. In a second alg, you finish the botom layer.

The second step is cycling the pieces. I was surprised when I saw that there "only" 12 case of 5-cycles with oriented corners (and there symmetry). So I decided to use it in the solve.

I'va made a table with the possibles cycles and how to solve it in two alg using 5-cycles, 3-cycles and 2*2-cycles :

Cycles Solution Comment
0 Corner in place
8 5-cycle + 3-cycle parity.
6 - 2 5-cycle + 2*2-cycle
5 - 3 5-cycle + 3-cycle
4 - 4 5-cycle + 5-cycle Use break into new cycles.
4 - 2 - 2 3-cycle + 2*2-cycle parity.
3 - 3 - 2 3-cycle + 3-cycle parity.
2 - 2 - 2 - 2 2*2-cycle + 2*2-cycle
1 Corner in place
7 5-cycle + 3-cycle
5 - 2 5-cycle parity.
4 - 3 3-cycle + 3-cycle parity.
3 - 2 - 2 3-cycle + 2*2-cycle
2 Corner in place
6 5-cycle parity.
4 - 2 3-cycle + 2*2-cycle
3 - 3 3-cycle + 3-cycle
2 - 2 - 2 2*2-cycle parity.
3 Corner in place
5 5-cycle
3 - 2 3-cycle parity.
4 Corner in place
4 3-cycle parity.
2 - 2 2*2-cycle
5 Corner in place
3 3-cycle
6 Corner in place
2 - parity.

Feel free to describe the method on your own websites and language as long as you link the original one. Some of you will probably explain it in English better than me !

Here are the algs : http://www.francocube.com/deadalnix/speedblind.php

Hi

Some questions (recall i do not BLD solve myself!!)

- The algs for your 5-cycles are almost same as 2 basic 3-cycles done qequentially - so what is the benefit in speed / otherwise ??

- Wouldn't it be much harder to "mentally remodel" what happens to the cube after a 5-cycle compared to doing it twice for 3-cycles.

- I guess setup scenarios would be much more complicated vs 3-cycles??

Would a combination of 5-cycles and finally 3-cycles be a good compromise for an overall corner solution? (compare this with various strategies for edge pairing on big cubes 6-2-2 vs 2-2-2-2-2-2 for example).

- Per

1/ For the benefit of using 5-cycles :
They're is two benefit in my opinion. Firstly you can execute the solution faster, and you need less recall during your solve and you minimize the pause for reflexion. Secondly (this word exist ?) you can just memorize what you are going to do during your solve and so the reflexion process is reduce.

2/ about "mentally remodel" as you need only 4 alg to solve the corner, just memorize the 4 alg you are going to do and execute it 1 second after blindfolded. You needn't any mental remodel because you memorize directly what you are going to do.

3/ About set-ups

In this method, set up are limited to an U and/or a D move. They are very simple. If you don't want to learn every alg, you can choose to do more complex set-ups. But the method can become really tricky in this way ! It's why I choose Pochmann's M2 to solve edges.

For edges, is definitively not a good solution. They're is too much alg to know if you want simple set-ups and too complex set-ups if you don't know enough algs.

Could you please explain your organization/categories? I think that would help us non-French speakers in finding which algorithm to use .

The article is wroteent in two parts :

The first one is 5-cycle for corners. It's this part we are interested in.

We have : "Etape 1, Orienter les coins." that means "step 1 : orient corners". After you can find differents algs to orient corner in two steps. The algs are the sames for the two steps. They are divised like that :
The alg to orient 1 corner on a face (plus eventulaly another on the opposite face), then 2 corners, then 3 and finally 4. In french : "1 Coin :", "2 Coin :", "3 Coin :", "4 Coin :" .

The second part is "Etape 2, placer les coins." in english : "step 2, permute corners".

First the break into new cycles is explaind. You'll fond a good explications of the technique on pochmann's website.

Then you'ill find differents 3-cycles algs : "Les 3-cycles", the 2*2-cycles : "Les 2*2-cycles" and finaliy the 5-cycles : "Les 5-cycles"

This seems like a good way of solving them, and i will try to look into this.

deadalnix: I think I was unclear in my question... I was wondering how you organized your 5-cycles. When I was trying to do some BLD solves with your method, it took me a while to find the right 5-cycle to use, but I am assuming that you organized your algorithms in a logical order.

Ok. Excuse me.

They are two big categories : 4/1 and 3/2 . The first one is 4 corner on top and 1 on bottom, the second is 3 corners on top and 2 on bottom.

For other cas, return the cube using z2 for example.

The alg are listed with a case and his symmetry.

The 3/2 cases are in sub categories :
type 1, 2 and 3. It refer to the cubies on the botom.
1 : you have to use the one near you, then the other in your cycle.
2 : you have to use the two corner in the other order
3 : the two corner on the bottom are diagonally opposed.

If you have another question

Thanks, that cleared up everything! However, I have one more question: in the corner orientation section, where are the cases with 2 diagonal corners misoriented?

They are not presented. I think these case needn't any alg because an F or F' as a set-up and you get a well known case.

Maybe I will add it in the future. Anyway, I don't use any specific alg for this kind of cases.

So is there someone who has mastered the algs? is there someone who uses this system??

for me, there are to much permutation algs.. is there a way do reduce the number of permutation cases??

Rémi

As far as I know, Deadalnix is the only one to use this. He told me that He achived sub20 times, I don't know if it was solving time or memo+solving time.

memo+solving .

Reducing permutations cases is possible easily using set-ups. Set-ups are realy hard to improvise in this method, but you can learn them. The number of case isn't so huge this way.

Don't be afraid of orientation cases : many alg are done using set-ups. It take me less than 1 week to master the orientation. Look at the orientation in last and solve it in first. Many case can be done in 1 alg, and all can be done in 2.

I'm not a realy fast cuber because I like to try many differents method. I can do the cube in 20-25s . I think that a fanatic cuber can be realy faster than me with this method.

20 seconds ?
With R2 or 3op I am still stuck at 35 seconds average... I still can't decide...