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 Post subject: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 7:34 am 
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I got Eitan's ETO yesterday, and don't want it to go a waste, anybody had any experience solving it or the Curvy Copter II as it is mechanically equivalent?

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 12:38 pm 
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You'll find a few hints about the Curvy Copter II here.
Especially Brandon's post:
bmenrigh wrote:
If you're going to go for as few moves as possible, I think the best solve order is:

0) Check for center parity to determine correct orientation for corners.
1) Helicopter cube pieces. Corners and wide-triangles in whatever way is the most efficient.
2) Thin triangles [[1:1],1] (8 moves) [LU, FL, LU, UR, LU, FL, LU, UR]
3) Centers [[1:1],[1:1]] (12 moves) [UR, FU, UR, DR, BD, DR, UR, FU, UR, DR, BD, DR]

The reason I advocate centers last is that there are only 6 of them but there are 24 thin triangles. It's better to use an 8-move routine for 24 pieces and a 12-move routine for 6 rather than a 4-move routine for 6 pieces and then a 12-move routine for the 24 pieces.

That is:
24 * 8 + 6 * 12 = 264
Versus:
4 * 6 + 24 * 12 = 312

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 1:40 pm 
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Thanks Konrad; I'm sure when I decide to scramble it this will help! Using this and the gelatinbrain applet I found a corner twisting algorithm, and a pure triangle wing 3 cycle, however each algorithm is over 100 moves :lol: So its only alright for virtual solving with macros :|

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 2:35 pm 
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JackRTully wrote:
Thanks Konrad; I'm sure when I decide to scramble it this will help! Using this and the gelatinbrain applet I found a corner twisting algorithm, and a pure triangle wing 3 cycle, however each algorithm is over 100 moves :lol: So its only alright for virtual solving with macros :|
Have you looked at the results of copying and pasting the sequences into 3.3.8?
I think, Brandon's advice is most efficient.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 2:39 pm 
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I'm not solving the Curvy Copter II, just its octahedral twin; therefore the centers on the CC II are what I referred to as corners so they have permutation. And the pure 3 cycle for the wings was not needed, I just found it for the fun of it :lol:

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 3:38 pm 
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The edge-wings are pretty hard to setup so I have a few different routines in my arsenal for a physical solve. Here is a 2-2 swap across opposite edges: [UR, UL, UR, DL, DR, DL] This winds up being pretty useful.

The shortest pure commutator I can find for twisting two corners is:
[UR, UF, UR, DR, DB, DR, UR, UF, UR, DR, DB, DR, UB, UF, UB, UR, UF, UR, DR, DB, DR, UR, UF, UR, DR, DB, DR, UB, UF, UB]
Edit: found a better one: [UF, UR, UF, RF, UF, UR, UF, RF, UF, UR, UF, RF, UF, UR, UF, RF, UF, UR, UF, RF, UF, UR, UF, RF]

Surely there is something shorter. I don't bother twisting corners pure though.

If you can afford to move the edge-wings this is shorter:
[UR, UF, UR, DR, DL, BL, DB, DR, UR, UF, UR, DR, DB, BL, DL, DR]
Edit: even better is [UF, UB, UF, RF, RD, DF, UF, UB, UF, FD, RD, FR]

I think you'll find the setups for the edge-wings quite challenging in a physical solve.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Thu Mar 21, 2013 7:20 pm 
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My last post probably wasn't clear.

Just so it's clear, I don't think it's helpful to think of this puzzle as a Curvy Copter II because the solve order for the CCII is not at all the solve order you want for Eitan's ETO.

For a non-jumbling solve, I suggest finding the fixed global orientation using the orbits of the wide triangles FIRST. If you don't do this you'll find that the puzzle is unsolvable without jumbling or starting over.

Then solve the wide triangles and corners at the same time. You can 3-cycle wide triangles with [UF, UB, UR, UB, UF, UB, UR, UB] and you can change the parity of two orbits with [UF, UR, UF, UR, UF, UR].

You can cycle corners with [UF, UB, UF, UB] and you can change their orientation with [UB, UF, UB, BD, DL, BL, UB, UF, UB, BL, DL, BD]

Then I'd solve all edge-wings with [UF, UR, UF, UL, UF, UR, UF, UL]

Then I'd finish the centers with [UF, UR, UF, FL, FD, FL, UF, UR, UF, FL, FD, FL]

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Mar 22, 2013 7:49 am 
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JackRTully wrote:
I'm not solving the Curvy Copter II, just its octahedral twin; therefore the centers on the CC II are what I referred to as corners so they have permutation. And the pure 3 cycle for the wings was not needed, I just found it for the fun of it :lol:
Aah, I had not looked at the ETO before and now I see that we have it in Gelatinbrain.
I thought you were talking about Helicopter corners. :roll:

Maybe, you want to add a little review of Eitan's ETO here?

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Mar 22, 2013 11:25 am 
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Konrad; I'm way ahead of you... Kind of... Maybe... Well I had planned to write it later on anyway is what I meant :lol:

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Mar 22, 2013 2:09 pm 
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bmenrigh wrote:
My last post probably wasn't clear.

Just so it's clear, I don't think it's helpful to think of this puzzle as a Curvy Copter II because the solve order for the CCII is not at all the solve order you want for Eitan's ETO.

For a non-jumbling solve, I suggest finding the fixed global orientation using the orbits of the wide triangles FIRST. If you don't do this you'll find that the puzzle is unsolvable without jumbling or starting over.

Then solve the wide triangles and corners at the same time. You can 3-cycle wide triangles with [UF, UB, UR, UB, UF, UB, UR, UB] and you can change the parity of two orbits with [UF, UR, UF, UR, UF, UR].

You can cycle corners with [UF, UB, UF, UB] and you can change their orientation with [UB, UF, UB, BD, DL, BL, UB, UF, UB, BL, DL, BD]

Then I'd solve all edge-wings with [UF, UR, UF, UL, UF, UR, UF, UL]

Then I'd finish the centers with [UF, UR, UF, FL, FD, FL, UF, UR, UF, FL, FD, FL]


When you had written that I had already solved the wide triangles, but I didn't check for "global orientation". What exactly does that mean?

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Mar 22, 2013 3:06 pm 
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JackRTully wrote:
When you had written that I had already solved the wide triangles, but I didn't check for "global orientation". What exactly does that mean?

The wide triangles on Eitan's ETO and the CCII and the Helicopter cube are all the same piece type. The 24 of them are in 4 orbits of 6 triangles each.

On the Helicopter cube and CCII there is one of each of the 6 colors in each orbit. This allows you to solve the triangles into arbitrary orientations (relative to the core).

On the ETO, they're in the same orbits (or course) but now each orbit only has 6 of the 8 colors. This means that not all orbits are equal and you have to solve them relative to each other which acts to define a fixed global orientation.

Try scrambling Gelatinbrain's 4.3.1 and then solving all of the triangles. You'll find that there is only one correct choice for each face color.

You have two options: find the right orientation, or use jumbling to move pieces between orbits.

It's the octahedral version of this http://www.twistypuzzles.com/forum/viewtopic.php?p=253852#p253852

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Mar 22, 2013 3:20 pm 
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bmenrigh wrote:
Try scrambling Gelatinbrain's 4.3.1


I had accidentally scrambled it by misreading an algorithm, and I JUST fully scrambled it. A physical solve is now due :scrambled: :mrgreen:

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sat Mar 23, 2013 5:52 am 
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I scrambled it again after solving it once, I have 2 corners needing to swap... Help?

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sat Mar 23, 2013 6:13 am 
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It's the same as swapping two centres on the Curvy Copter II, right? Another quote from that thread:
bmenrigh wrote:
77mouser wrote:
I got it solved! Thanks! :D

I'm still looking for algs that cycle the centers pure though. Can anyone help me out?

If you want a routine that swaps two centers pure that's impossible by definition. To resolve the odd permutation parity everything else must be moved around the centers rather than the centers swapped. If you accept that as "pure" of course a routine exists but I'm not aware of a short or efficient one.

Maarten's cyle is a 2-2 swap which is an even cycle just like a 3-cylcle.

If you want a 3-cycle there is a simple [[1:1],[1:1]] (12-move) sequence:
[UR, FU, UR], [DR, BD, RD], [UR, FU, UR], [DR, BD, DR]

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sat Mar 23, 2013 12:08 pm 
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JackRTully wrote:
I scrambled it again after solving it once, I have 2 corners needing to swap... Help?

Did you use jumbling moves? I'm struggling to see how this parity issue (hidden global orientation) can be achieved without jumbling.

How far along in the solve are you? That is, which piece types are completely solved already? For a non-jumbling solve I determine the orientation using the wide-triangle orbits and then solve the wide-triangles and corners first. For a jumbling solve, I solve the corners first to define the color scheme and then solve everything to that (wide triangles then wings then centers).

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sat Mar 23, 2013 1:06 pm 
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I've completely scrambled it including jumbling now, oh dear :(

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sat Mar 23, 2013 1:39 pm 
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JackRTully wrote:
I've completely scrambled it including jumbling now, oh dear :(

Alright just solve all of the corners relative to each other, then check that you're able to solve all of the big center triangles (I'm not sure this check is actually needed due to the orientation of the corners but check anyways). Once you have all of the corners solved and determined all of the center triangles can be solved, you can then start solving the puzzle into that color scheme (global orientation). You'll have to use jumbling moves to get the wide triangles between orbits.

The overall solve will only be harder at the beginning. The rest will be the same.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 6:21 am 
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Apologies for the bump, but if I am unable to solve the big center triangles, what have I done wrong?

Edit: I just came across this problem

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 8:41 am 
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JackRTully wrote:
Apologies for the bump, but if I am unable to solve the big center triangles, what have I done wrong?

Edit: I just came across this problem
I think you should provide more information, e.g. photos of all faces.
I guess you are not talking about a situation you can solve by the pure 3-cycles Brandon has shown above?

[UF, UR, UF, FL, FD, FL, UF, UR, UF, FL, FD, FL]
Result on a solved ETO

Image

So, I assume, you see an odd parity of the centres? (E.g. a swap of two centres is needed?)
Everything else is solved?
Have you jumbled it?

Please, describe your situation precisely.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 8:44 am 
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I had jumbled the puzzle, I realize I can solve it fine without jumbling! I would take pictures but I'm currently assembling it again, I find it too difficult too solve with jumbling moves :(

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 9:29 am 
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P4120002.JPG [ 2.83 MiB | Viewed 3360 times ]


Here you can see I need a 2-2 swap of he edge wings, the centers are fine; all the set up moves and 3 cycles seem to be useless.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 9:44 am 
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Now you are showing a different problem than on 12:21pm. (You talked about problems with centres then).
Any 2-2 swap of pieces is an even permutation and you should be able to solve it with two 3-cycles and setup moves.

E.g.
1234 is the target ordering. you are at 2143 (1 <->2 and 3 <-> 4 necessary)
First 3-cycle=> 1423 (1 -> 2 -> 4 -> 1)
Second 3-cycle=> 1234 (2 -> 4 -> 3 -> 2)

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 9:49 am 
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No, that center problem was due to jumbling, I'm going to see if I can solve these edge wings now :D I've now memorized all algorithms to solve this without jumbling :D

EDIT: I understand 3 cycles and setup moves should theoretically work; but I can't seem to set the pieces up without moving other wings in the way

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 10:05 am 
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You should cycle one in place so there are only three left. Solving the last three at once could take 10+ setup moves.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 11:40 am 
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As an example I used your earlier picture and show you a setup + 3-cycle sequence:
Image
The sequence UB, RB, UR, RF, RB, BL, DR, RB, DR, RF, DR, RB, DR, RF, BL, RB, RF, UR, RB, UB in Gelatinbrain notation is performed on a solved ETO at the right.
Just check it by cutting and pasting it into Gelatinbrain 4.3.1
It will put one edge wing in your photo to the right place.
I find the Gelatinbrain octahedron notation is not very easy to memory. Once you understand how the corners are labelled, it is not so bad in this case.

The first six moves are setups followed by Brandon's 3-cycle from above just with a different orientation.
In commutator / conjugate notation: [UB:[RB:[UR:[RF:[RB:[BL:[[DR:RB],RF]]]]]]]

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 11:58 am 
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Just in case it sounds like I think the setups on this puzzle are easy... When I solved it I posted at http://twistypuzzles.com/forum/viewtopic.php?p=241299#p241299

bmenrigh wrote:
Did others find the setup moves for the edge-wing pieces quite numerous and challenging on 4.3.1 and 4.3.6 or am I missing something obvious?


Julian responded in http://twistypuzzles.com/forum/viewtopic.php?p=241458#p241458 with:

Julian wrote:
They are tricky, but I think the "worst case scenario" is 9-10 setup moves


If you ask me, ~10 setup moves is pretty awful.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 12:12 pm 
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bmenrigh wrote:
Just in case it sounds like I think the setups on this puzzle are easy... When I solved it I posted at http://twistypuzzles.com/forum/viewtopic.php?p=241299#p241299

bmenrigh wrote:
Did others find the setup moves for the edge-wing pieces quite numerous and challenging on 4.3.1 and 4.3.6 or am I missing something obvious?


Julian responded in http://twistypuzzles.com/forum/viewtopic.php?p=241458#p241458 with:

Julian wrote:
They are tricky, but I think the "worst case scenario" is 9-10 setup moves


If you ask me, ~10 setup moves is pretty awful.



The relief you've just given me Brandon, I thought I was just stupid! :lol:

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 12:15 pm 
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JackRTully wrote:
The relief you've just given me Brandon, I thought I was just stupid! :lol:
Nope. We both are :lol:

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Fri Apr 12, 2013 1:30 pm 
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Oh my God! I did it! I'll probably scramble it again some time soon, but for now, thank you SO much Brandon & Konrad! :D

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Mon Jun 10, 2013 9:45 am 
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I have 2 edge wings needing to swap, is this a jumbling parity? I thought this was impossible.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Mon Jun 10, 2013 12:25 pm 
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It's a 2-2 swap, a pair of edges need to swap as well as 2 centres. Though I don't know how to solve this

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Mon Jun 10, 2013 12:49 pm 
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JackRTully wrote:
I have 2 edge wings needing to swap, is this a jumbling parity? I thought this was impossible.

Not all of the corners are solved. You can change the parity of the edge wings with a single edge turn. This also changes the parity of the corners.

Do an edge turn which will fix the parity and the re-cycle the broken edge-wings.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sun Jun 16, 2013 9:17 am 
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Two corners need to swap; everything else on the puzzle is solved. How can I do this relatively quickly with jumbling?

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sun Jun 16, 2013 10:20 am 
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JackRTully wrote:
Two corners need to swap; everything else on the puzzle is solved. How can I do this relatively quickly with jumbling?

I think this is a case of the whole color scheme rotated 90 degrees. I'm pretty sure it's impossible to swap those corners while leaving everything else intact. Instead I think you have to assume one of the incorrect corners is actually the only correct piece on the whole puzzle and re-solve everything around it.

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 Post subject: Re: Solving Curvy Copter II/Eitan's Edge Turning Octahedron
PostPosted: Sun Jun 16, 2013 10:27 am 
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Luke wrote:
It's much quicker to solve it with jumbling, provided you happen to stumble across convinient algorithms, which is what happened to me.


Referring to 2 centers swapped on the CCII

I'll ask him now and post his reply after.

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