Edge cycle insertions

[fanwuq]

What are some pure edge 3 cycles and edge 2 cycles that take fewer moves than Z, H, and U perms (let’s just say less than 9 moves HTM) that I can do right after orienting edges for Petrus? They should be convenient to do without much set up.

Thanks.

 

[blah]

Is it possible to further clarify your question?

What do you mean by pure edge 3 cycles or edge 2 cycles? Do you mean only the edges are cycled and the rest of the cube remains the same at the end of the cycle? If so, the minimum move count would be 8 moves STM commutators. And I don't really understand what you mean by edge 2 cycles, sorry.

Also, I don't understand why you want to do edge cycles after orienting the edges for Petrus. Wouldn't the next step be to extend the 2x2x3 block?

 

[Lotsofsloths]

Also, I don't understand why you want to do edge cycles after orienting the edges for Petrus. Wouldn't the next step be to extend the 2x2x3 block?

What are some pure edge 3 cycles and edge 2 cycles that take fewer moves than Z, H, and U perms (let’s just say less than 9 moves HTM) that I can do right after orienting edges for Petrus? They should be convenient to do without much set up.
Thanks.

All he wants are some really short HTM EPLL's.
I suggest opticubes.com for that though.

F B' E2 S L' S2 L E2 = Z perm
B2 U/U' M U2 M' U/U' B2 = U perm
U F2 M2 F2 U' F2 M2 F2 = H perm

 

[fanwuq]

I'm not sure how to word this.

Basically, I'm going to try this in FMC. I will do petrus F2L. Then, COLL. So I'll end up with a Z, H, or U perm. These algorithms aren't very short. 3 cycle is U perm. 2-cycle is H or Z.
In FMC, I would get to this step, see which pieces need to be switched. Undo all the moves until I get to near the beginning, where I can swap the edges using a shorter alg.
I'm rather inexperienced with this, so I'm not sure what to do here actually. I'm not sure when it will be a good opportunity to do this, but I assume it should be right after you orient the edges. When, the position is good, apply the alg, finish F2L and COLL, and end up with a PLL skip.

 

[Kenneth]

No algs shorter than 9 in HTM, but in STM you got these:

(x') M' U' R U M U' R' U (x) (8)... add mirror and inverses and you got four algs.

M U M' U2 M U M' (7) ... also mirror (or inverse, it makes the same)

The last one is my favorite ELL case, its so fast...

 

[fanwuq]

Well, the pieces don't have to be on one layer.

And your algs changes orientation.

I guess I'm not wording it correctly. I want the shortest alg that doesn't change the orientation, but the pieces don't have to be on the same layer, but it should not destroy the 2x2x3 block either.

Edit:

For 3 cycle, I mean something like

y' M U2 M' U2 y

Are there more short ones like it?

(Make sure it does not destroy the petrus 2x2x3 block!)

 

[ch_ts]

(R2U2)*3 (6 moves htm) switches UF with UB and RF with RB

and a 3-cycle with 3 edges in a middle layer:
- FB'R2F'BU2 (6 htm, 4 stm)
- FR2F'BU2B' or mirror image (6 htm, 5 stm)

another 3-cycle:
UF2L2B2DB2L2F2 (8 moves htm)

(with your 2x2x3 placed at LD)

That's all I can think of. Hope they help.

 

[fanwuq]

Good! I didn't know the last one!

Any others?

 

[Kenneth]

2x(M2 U2)

R U2 R2 U2 R2 U2 R

M' S' U' S U2 M U' ... well, it's short in STM =)

 

[Kenneth]

Here is another weird one: you kow about the cycle M' U2 M U2, lets say you want to follow that up with a S' U2 S U2 (same cycle but from a diffrent angle), then you can merge the two algs to one like this:

M' S' U2 S M U2 ... two three cycles in 6 turns

7x, same alg ... 5M is the widest slice (5 layer), 3M is the second (3 layer) and M is the single middle one, same for S-turns:

5M' 3M2 M2 5S' 3S2 S2 U2 S2 3S2 5S M2 3M2 5M U2 ... 10 three cycles in 14 turns