I can solve a curvy copter, a skewb, and unjumble the CCS but I just cannot figure out a pure 3-cycle for the two triangular edge pieces on the Curvy Copter Skewb. I've been working on this off and on for about a month now and I must have tried all the wrong ways to solve this puzzle. Any and all help will be greatly appreciated.

I haven't worked out a solve-order for this puzzle however looking at it using Gelatinbrain's program (it's puzzle 3.6.9) I'd solve them very early with a [1,1] commutator like [RBD, UR, RBD', UR]

If you can afford to move the triangles / shields (which are easy to cycle pure) and the slivers then this should help you:
[RBD', UR, RBD, FU, DFR', FU, RBD', UR, RBD, FU, DFR, FU]

Here is a pure sequence for shields:
[RBD', UR, RBD, DFR, FU, DFR', RBD', UR, RBD, DFR, FU, DFR']

And there is a simple non-pure (shield + sliver) [3,1] cycle.

A pure 3-cycle for those CC center-edges is going to be long and hard to find. I'll search for one if you really want to them pure.

Okay that makes a lot of sense. I was trying to group skewb corners (the corner, sliver, and triangle edge) and then solve the curvy copter part. the pure shields 3-cycle will definitely come in handy, thank you. And please do not look for a pure 3-cycle for the edges, I was just making sure I was not missing a simple way to do so. So the new strategy is solve curvy copter edges with triangle edges first.

Borrowing a bunch of insights from Daniel Kwan (DKwan) (including a conversation with him via the IRC channel) and looking at this further, I'm semi-convinced that the shortest pure "standard form" commutator for those pieces is [9,1] (20 moves).

I'd suggest thinking about reducing to a Curvy Copter as the solution strategy. Check for corner twist early. Other than corner twist I think you won't run into any trouble with a reduction solve.

Agreed! Also I am amazed that people can come up with commutators like that, especially on "skewbic" puzzles. However if you don't mind I would like to see that commutator just for fun .

Sure:
[RBD, FDL', RF, DF, RD, DF, RF, FDL, RBD', UR, RBD, FDL', RF, DF, RD, DF, RF, FDL, RBD', UR]

If you haven't seen my http://www.brandonenright.net/cgi-bin/gb_util.pl program then go ahead and paste in in there. It'll tell you the "form" of the commutator.

Before you look at a 20-move routine and think it's something special, understand that finding it took almost no thought. All I did was look at ways to separate the piece you want to cycle from the adjacent pieces. Once you look at it from that perspective it's easy to come up with a variety of 20-move sequences.

Brandon, could you post an image of the CCS with labels so I can understand better what you're referring to as shields, slithers etc

I made the title of this topic more general.
I wrote here back in DecemberI did not have the time to solve it very often.
Reduction to a Curvy Copter seems quite natural and this is what I did:
1. Group the twelve groups of four edge pieces to Curvy Copter edges (i. e. reduction to a Curvy Copter with scrambled centres)
a. small edges with two stickers
b. large edge pieces with one sticker
2. Solve the outer centre pieces (those adjacent to a corner) by moving around pairs of centres (i.e. centres of the Curvy Copter) You can do this with Curvy Copter jumbling moves. I prefer a combination of Skewb and Helicopter turns as on a Helicopter Skewb.
3. Solve the inner centres using pure 3-cycles
4. We have now a fully reduced Curvy Copter. If you have reduced the centres at the correct location, only the corners are remaining.

This picture explains the names I'm using in relation to Brandon's names:

I invented my own notation, but I'll use here Gelatinbrain notation. Faces are named as on a normal 3x3x3 and two letters denote a Helicopter turn (e.g. FU), three letters a vertex Skewb turn (e.g. DRB = clockwise 90° turn around vertex Down/Right/Back)

As Brandon pointed out, you will check for a single twisted corner very early (= Helicopter corner solve) and build the twelve edges at there correct location.

I prefer to start with the `small edges` with two stickers, because I find this visually easier, doing [1:1] conjugates to swap two edges.

For the `large edges` I found three impure 3-cycles.

I'll show the sequences and a picture showing the result when I start with a solved puzzle:
1.b.1 [[RBD':UR],[ULB:FL]] ( as [[1:1], [1:1]] commutator ) or explicitly
[RBD', UR, RBD, ULB, FL, ULB', RBD', UR, RBD, ULB, FL, ULB']


1.b.2 DFR', RBD', DFR, RBD, DBL, RBD, DBL', RBD', FU, RBD, DBL, RBD', DBL', RBD', DFR', RBD, DFR, FU


1.b.3 RD, BRU, LUF', BRU', LUF, DBL, DFR', LUF, DFR, LUF', DBL', RD, DBL, LUF, DFR', LUF', DFR, DBL', LUF', BRU, LUF, BRU'


The sequence above I have found first. It is based on a normal Skewb Corner twist - I took it over from Julian a long time ago - and its inverse, a [10,1] commutator.

If you start with the `large edges`, here is Brandon's 3-cycle for the small edges above:
[[RBD':UR],[FU:DFR']] or
[RBD', UR, RBD, FU, DFR', FU, RBD', UR, RBD, FU, DFR, FU]


And here is the 20 move pure 3-cycle:
[[RBD:[FDL':[RF:[DF:RD]]]],UR] or
[RBD, FDL', RF, DF, RD, DF, RF, FDL, RBD', UR, RBD, FDL', RF, DF, RD, DF, RF, FDL, RBD', UR]


The reduction of the Curvy Copter centres is pretty straight forward.
I prefer to have them at their final location and solve the outer centres first in step 2.
e.g. via [[DFR:UR],UB] or
[DFR, UR, DFR', UB, DFR, UR, DFR', UB]


A pure 3-cycle for the inner centres (`shields`):

[[DFR:FU],UR] or
[DFR, FU, DFR', UR, DFR, FU, DFR', UR]



EDIT: Just for fun I tried to find a pure commutator for a Large-Edges 3-cycle:
[[[ULB:RBD']:[[ RD DL]:DF]],UR] or
[ULB, RBD', ULB', RD, DL, DF, RD, DL, ULB, RBD, ULB', UR, ULB, RBD', ULB', DL, RD, DF, DL, RD, ULB, RBD, ULB', UR] 24 turns; a [11,1] commutator
Brandon will probably find a shorter one.
Nobody really needs this



EDIT2: BTW, if you look carefully at my avatar, you can probably recognize the puzzle in the little girls hand?

In this algorithm (and the rest), which face is U, R, F etc ?

Apologies for the bump

Three letters like RBD' would be a skewb vertex twist.
Two letters like UR would be a helicopter edge twist.
U, R, F etc are the same as an RC.

I know that.
But, look at the image for the 3 cycle. Which face (red, white or green) should be designated U, F or R for the algorithm to work?

Try U as white, F as Green, and R as Red.

That doesnt seem to work...

All my pictures / diagrams show the same colour situation U = white F = green R = red.
I double checked the sequence
RBD', UR, RBD, ULB, FL, ULB', RBD', UR, RBD, ULB, FL, ULB' (12 turns - a [[1:1],[1:1]] commutator) in Gelatinbrain 3.6.9 and it does what it is supposed to do

There must be a problem with the interpretation of the notation (Gelatinbrain's).

Single letters denote faces (but never turns)
Three letters denote a vertex turn: RBD is the vertex at Right/Back/Down turned clockwise by 120°; RBD is the same vertex turned counterclockwise.
The edge turns should be clear?
Can you run Gelatinbrain?
Do you know Brandon's sequence utility?

This would produce a disassembly of the 12 moves as [[RBD':UR],[ULB:FL]]
I think you are familiar with the commutator/ conjugates notation?

If really necessary, I can make a move sequence of the twelve moves, but that is a lot of work.
(I do not have video equipment.)

EDIT:
I have made a sequence using Gelatinbrain 3.6.9.
It starts with a solved Cube and is followed by 12 diagrams for the 12 moves.
Each diagram shows all faces in the usual frontview/backview fashion of Gelatinbrain.
Each single turn is followed by the resulting situation, left to right, top to down.
I hope this helps.


You can click onto the picture to enlarge it.

EDIT2: No reaction, are you still lost?
Here are 4 pictures showing the four turns involved in midturn on a physical puzzle (RBD, UR, ULB, FL)



EDIT3: Just to be sure that the notation is interpreted correctly:
In all notations I know of, the apostrophe stands for anti-clockwise. E.g. WCA notation:

Apologies for yet another bump, but I ran into another weird parity while doing a jumbling solve.

It is a 2 corner swap. (Or a 1 center flip if you wish)

Any tips? What happened?

These sorts of issues are the gems of solving that make it all worth it. I'd hate to ruin the experience of figuring this situation out so I break this up into hints for you.

Hint 1: [You've already spotted that two corners swapped is the same as a single edge-center group flipped. If you solve the corners you have to flip the edge-center group.]

Hint 2: [You know, even with jumbling, that there are always two small edges in the edge-center group so no mater how much you jumble the puzzle, and edge-turn swaps them and changes the parity of the small edges.]

Hint 3: [Changing the parity of the small edges is the same as flipping and edge-center group. Every edge turn always changes their parity but there is a case while jumbling where an edge-turns does not change the parity of the corners.]

Hint 4: [The corners are equivalent to another piece type on the puzzle. You can use that to change the parity of the corners (and flip a edge-center-group), and then put the equivalent pieces in the corner spots, and re-flip the edge-center group.]

Hint 5: [Use two identically colored inner center (shield) pieces because you can't see a swap of those. The inner center pieces are essentially the same as corners when you jumble.]

I'd demonstrate on my print but the pieces are all encased in super glue right now.

Edit: I changed the names of the pieces to match Konrad's names.

I'm confused a bit and I guess it has to do with names. I used these names before:
"
Center" (= centre in BE) would mean a composed Curvy Copter centre = "inner centre" + "outer centre".
I guess, "1 center flip" refers to a flip of the centre of rotation = Curvy Copter edge?

So far, I had assumed that a Curvy Copter Skewb can be solved after unjumbling just using doctrinaire (i.e normal, non-jumbling Helicopter and Skewb) moves.
I understand this is not true, right?

Your situation is: Everything is solved, just two corners are swapped?

I was so intimitated by my failure to unjumble the Unbandaged Helicopter Skewb that I never dared to jumble the Curvy Copter Skewb.

EDIT: I tried to swap two corners on a Curvy Copter, but I end up with a flipped edge:


So, I guess your problem has to do with Skewb jumbling turns.

I updated my hints to use your names. I agree having a standard people follow helps

I really hope you revisit the jumbling on these puzzles. If you want to work on things in order of difficulty I'd suggest:

Helicopter Cube / Curvy Copter. You have to get very comfortable with the jumbling to the point where any situation you find yourself in you immediately know how to fix. Absolutely no "guess and check unjumbling" or random turning.

Unbandaged Helicopter cube (just don't use any Skewb turns or use Eric's puzzle). The unbandaging makes things get crazy quick. At first unjumbling will consist of random guessing almost exclusively and as you become more comfortable with corners swapping with inner centers and dealing with twisted inner centers you'll find unjumbling it pretty fun and easy.

Helicopter Skewb or Curvy Copter Skewb. This introduces the jumbling of the Copter edge-centers which are tricky at first. I prioritize unjumbling the edge-centers before unjumbling the rest of the puzzle.

Unbandaged Helicopter Skewb. This combines all of the issues into one crazy jumbling experience. It actually isn't much harder than the Helicopter Skewb or Unbandaged Helicopter cube. The additional jumbling freedom makes for mind boggling situations but also allows for much more unjumbling freedom.

I addressed this case in September with "Edit 2" of viewtopic.php?p=287719#p287719

It doesn't have to do with "Skewb jumbling turns" so much as what Skewb Turns do to the normal Curvy Copter jumbling state. With only Curvy Copter jumbling these corner + inner-center groups always stay together:
It isn't possible to get into a situation where the highlighted region doesn't contain a corner. This means that every edge turn always swaps two corners. When you add the Skewb turn, you can split these corner + inner-center groups which allows you to get into a situation where an edge turn doesn't swap two corners.

This discussion motivated me to look at "Helicopter jumbling" (in a generic sense) again.

I have jumbled and solved the Curvy Copter and Helicopter Cube often in the past. Actually, I got the Curvy Copter three years ago and it was my first jumbling puzzle ever. I revisted it during my Christmas holidays.

Thanks for your list. I'm just not sure if I will ever become a jumbling fan like you

I feel that doctrinaire twisty puzzles are based on real sience (group theory), while jumbling has the touch of "try and error" and ad hoc intuition. Just my opinion.

Maybe I'll change my opinion, if our friend bhearn returns and solves a jumbled Helicopter Skewb. (bhearn had given it up and I judge his solving capabilities as outstanding.)Do you mean, I should use Luke's Curvy Copter Skewb (CCS) without Skewb turns? (I have not got Eric's Unbandaged Helicopter Cube and the Original (not Unbandaged) version of Tom's Helicopter Skewb.I think that the Curvy Copter Skewb would be the easier choice, because I can see the edge jumbling directly. (bhearn had wanted a transparent Helicopter Skewb. Maybe, he would be pleased with the CCS?

rubikcollector123, would you mind to elaborate the other weird parities?

The 1 corner orientation parity (not jumbling but still a parity) and the 1 corner-sliver-shield block thats out of shape parity. (that one i know how to fix)


Speaking of which, what happens if one replaces all the shield pieces with corner-sliver blocks and sanded it back to cubic?

We don't have an agreed-upon name for this sort of problem but "parity" isn't it. I often call it "excess twist".

I'm inclined to say you'd be sanding pieces closer and closer to the spherical version of the puzzle.

The Bump created an interesting conversation and I hope others will find it interesting as well.Obviously, you mean a situation like this (the invisible part is all cubic):

Interesting question: Should we call this a parity?
We had several discussions about the term "parity" (most recently here and I know we should not be completely mathematically puristic about saying "This is a parity". Let me repeat the Wikipedia definition:When cubers say "This is a parity" they mean that an odd number of swaps (in group theory "transpositions") in a group of pieces (piece types) is necessary to get to the solved state. The solved state when unjumbling is the cubic shape.
While unjumbling, we care about shape only and we can consider the paired "corner+sliver piece" to be in the same piece group as the "shield". Therefore, the term "parity" is justified. We need a single swap to reach the final cubic shape.

Anyway, we should use the word "parity" describing an permutation issue, only.
(The flipped edge parity on the 4x4x4 is a "parity error" when viewing the 4x4x4 as a reduced 3x3x3. Actually, it is a swap of two 4x4x4 edges.)

I have now swapped two corners on an otherwise solved cube:

Thanks to Brandon's hints even I - a jumbling novice on this cube - was able to do this.
I do not have a short sequence, more a recipe - not more than in Brandon's hints.

rubikcollector123, if you are still having problems, I could make a picture sequence.
The CCS is not very much scrambled by following this recipe, a few pieces have to be relocated by doctrinaire moves afterwards.

EDIT: Here is the situation after a few (36) moves:

If we agree upon a notation describing jumbling moves, I can write it down for you.
I use <X>j for a clockwise turn of X to the next jumbling position.
E.g. URBj would be a jumbling Skewb turn of vertex URB and URBj' would be the reversed turn.