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 Post subject: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Mon Feb 17, 2014 11:31 pm 
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Mine came in the other day and I've finally had a minute to play with it. I think I'm one of the few to like the fish eyes. If anything, it makes it easier to describe pieces.
It's a nice additional challenge to the curvy copter. It turns well, however when the fish eyes are jumbled and rotated, the puzzle catches a lot, so one has to be careful. I'm still sorting out different algorithms to try to shuffle around the fish eyes, corners and the pieces between them. As posted in the "almost there" thread http://twistypuzzles.com/forum/viewtopi ... =8&t=26891 I'm down to one corner and one fish eye needing rotation.

Good, fun puzzle for <$40 US

-d

[Moderator]I have split the more solving related posts to this new topic.
So, people can more freely contribute their thoughts about solving this puzzle.[/Moderator]


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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Fri Feb 21, 2014 11:01 am 
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darryl wrote:
It turns well, however when the fish eyes are jumbled and rotated, the puzzle catches a lot, so one has to be careful.
I just received mine this morning and I played with the jumbling a little, and I think (actually I am sure) it fudge. See the images bellow.


Attachments:
File comment: jumble move
IMG_20140221_105011.jpg
IMG_20140221_105011.jpg [ 1019.04 KiB | Viewed 3810 times ]
File comment: close up, the pieces are pushed from the center
IMG_20140221_105239.jpg
IMG_20140221_105239.jpg [ 1.06 MiB | Viewed 3810 times ]

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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Fri Feb 21, 2014 2:35 pm 
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Anyone else end up with one edge piece flipped? I've solved this puzzle a few times now and this is the first time that this has happened. Is this a valid state or did I fudge something along the way?


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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Fri Feb 21, 2014 2:43 pm 
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Yes, it's possible, but I ended up with only one corner twisted!


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 Post subject: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Fri Feb 21, 2014 10:12 pm 
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andand wrote:
Yes, it's possible, but I ended up with only one corner twisted!

Those little pieces act as corners when the puzzle is jumbled :p.

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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Sun Feb 23, 2014 5:21 am 
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andand wrote:
Yes, it's possible, but I ended up with only one corner twisted!
Can one corner really be twisted on its own? I could manage this only, when a triangle is twisted as well:

Image

As you can see on this close up, one yellow triangle is twisted counter clockwise, while the URF corner is twisted clockwise.

Image

Before I dare to scramble this puzzle thoroughly, I would like to know how hard it is compared with the Helicopter Skewb?

Brandon, do you hear me?
I would love to view one more of your wonderful videos about unjumbling the Curvy Copter Plus! :)

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Mon Feb 24, 2014 3:51 am 
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Hi Konrad,
perhaps I should continue solving puzzles. This looks very interesting.
Is it very different to Helicopter cube ? I do not own a curvy copter.
Is it hard to solve ? I ordered it two days ago, together with Pitchers Octocube.


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Mon Feb 24, 2014 1:11 pm 
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Andrea,
I would say The curvy copter is one step more difficult than the helicopter. Then the Curvy Copter Plus is one step more difficult than the Curvy Copter.

So I was thinking, maybe it is possible to have one of the center pieces rotated. What if some of the center pieces were swapped for the same color, then couldn't it be possible for one of them to be out of place?

-d


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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Mon Feb 24, 2014 1:28 pm 
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Konrad wrote:
Brandon, do you hear me?
I would love to view one more of your wonderful videos about unjumbling the Curvy Copter Plus! :)

I can hear you :-) For some reason California always seems to be last in line to get shipments. You Europeans usually have the puzzle at least a week before me. My print of TomZ's Curvy Copter Plus is partially tumbled but on indefinite hold while I try to clear my very long backlog of more important things to tumble :? .

You are right that a single corner can't be twisted all by itself. You will always have a twist in a small triangle exactly like how you've shown. Furthermore, if the corner is twisted CW then the triangle will be twisted CCW, or vice-versa.

It's also possible to have 2 corners swapped, pure, or a single edge flipped, pure. The solution to these cases is identical to the hints I posted in this thread. Hint: small triangles are corners and there are identical small triangles which allow for permutation trickiness.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Mon Feb 24, 2014 3:21 pm 
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Hi Andrea,

I was skiing all day, so Darryl has already responded to your post. :)
I got TomZ's 3D-printed Curvy Copter first (a beautiful puzzle by all means), so I had solved that one before I got Jason's Helicopter Cube. I do not see that the Curvy Copter is more difficult than the Helicopter. The only difference is that the edges are exposed. Jumbling is what makes both more difficult than solving them without jumbling!
The Curvy Copter Plus jumbles like hell. I think everybody will do it the same way:
1. Reduce it to a CC (cubic, centres not yet in their correct orbits)
2. Solve the CC
Andrea wrote:
Hi Konrad,
perhaps I should continue solving puzzles. This looks very interesting.
Is it very different to Helicopter cube ? I do not own a curvy copter.
Is it hard to solve ? I ordered it two days ago, together with Pitchers Octocube.

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 Post subject: Re: Mefferts Curvy Copter Plus
PostPosted: Wed Feb 26, 2014 4:36 pm 
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Brandon Enright wrote:
...
It's also possible to have 2 corners swapped, pure, or a single edge flipped, pure. The solution to these cases is identical to the hints I posted in this thread. Hint: small triangles are corners and there are identical small triangles which allow for permutation trickiness.
I didn't look at the details of that old thread. I'm not so much afraid of such special situation as of the complete chaos of a thoroughly jumbled puzzle.
(The Unbandaged Helicopter Skewb was a disaster for me :oops: OK, I tried it once only, because I had assembled and stickered it for Burgo :) )

Two swapped corners:

Image

One edge flipped:

Image

Any opinions how hard the Curvy Copter Plus is, compared with the Helicopter Skewb / Unbandaged Helicopter Skewb?

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 4:20 am 
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I haven't contributed yet and I only received mine today. I'm kerflummoxed. That means I have no real idea, and it will come across like that in the unboxing video I put out. I can see how the petals have been split, but I'm finding it difficult to work out how to properly separate the centers and petals. Can it be jumbled but kept in cubic shape? (like the curvy copter can be). I'm really worried that if I start jumbling properly I'll never get it back. But then I saw some others have solved it a number of times. Is it more bark than bite? :?

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 4:43 am 
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Rline: on Redkb video that solves the curvy copter plus shows a way using a few setup moves to swap two center triangles and the undo the setup moves to become a cube, looks very straighforward!

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 8:07 am 
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To answer my own question above:
It is certainly easier than the Unbandaged Helicopter Cube, because you can immediately see the pieces in full shape, while on the Unbandaged Helicopter Cube the jumbled parts are hidden.


I find things like the swap of triangles in my picture below pretty straight forward:

Image

The harder problems come up in a completely chaotic situation.
I scrambled the puzzle pretty thoroughly this morning.
The pieces started to catch so badly that even in a more or less cubic form the doctrinaire 180 degree turns became hard to do on a physical level.
This is somewhat frustrating, when you logically perfectly know what you want to turn, but it takes a lot of time to do the physical turn.
Darryl has expressed a similar observation in the top post of this thread.
darryl wrote:
It turns well, however when the fish eyes are jumbled and rotated, the puzzle catches a lot, so one has to be careful.
Sometimes it felt like I was trying illegal turns.
And then it popped pretty badly. I have assembled it completely to the solved state.
The good news: This is not very hard. You do not need to unscrew anything. I wouldn't know, if the caps come off, anyway.

When I scramble it the next time, I will jumble it a bit less.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 8:59 am 
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Am I the only one who has has had the screws unscrew themselves?
I had to buy screws to replace these loose ones. :evil:

I miss starting with the white side!

P.S I think that some of you may be having corner-twists on the center triangles. I find this puzzle solves much like a megaminx.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 12:06 pm 
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Konrad wrote:
The harder problems come up in a completely chaotic situation.
I scrambled the puzzle pretty thoroughly this morning.
The pieces started to catch so badly that even in a more or less cubic form the doctrinaire 180 degree turns became hard to do on a physical level.
This is somewhat frustrating, when you logically perfectly know what you want to turn, but it takes a lot of time to do the physical turn.
Darryl has expressed a similar observation in the top post of this thread.
darryl wrote:
It turns well, however when the fish eyes are jumbled and rotated, the puzzle catches a lot, so one has to be careful.
Sometimes it felt like I was trying illegal turns.
And then it popped pretty badly. I have assembled it completely to the solved state.
The good news: This is not very hard. You do not need to unscrew anything. I wouldn't know, if the caps come off, anyway.

When I scramble it the next time, I will jumble it a bit less.

Both of you are cheating :D You're catching on overhang bandaging. On this Curvy Copter Plus the inner triangles are so small and nearly triangular that the overhang bandaging is very minor. On an Unbandaged Helicopter Cube the overhang bandaging is much more significant and you can't push your way through it like you're doing on this puzzle.

Don't force through any overhang bandaged turns. If you do, the turning is poor and the solving is too easy. It's a lot trickier to let the bandaging let you work yourself into a corner where only one edge can be turned. Resist the temptation to push through the bandaging in those situations!

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 3:18 pm 
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Brandon Enright wrote:
Both of you are cheating :D You're catching on overhang bandaging. On this Curvy Copter Plus the inner triangles are so small and nearly triangular that the overhang bandaging is very minor.

From my limited play, I thoroughly agree with this and know exactly what Brandon means. I noticed that it very slightly "pushes" the triangle, almost so slightly that you're tempted to assume it's "normal".

Konrad wrote:
To answer my own question above:
It is certainly easier than the Unbandaged Helicopter Cube, because you can immediately see the pieces in full shape, while on the Unbandaged Helicopter Cube the jumbled parts are hidden.

I'm sure that would mean something if I had any experience at all with the unbandaged helicopter cube.

From some subsequent comments, I think it seems probably harder than I originally thought. In other words, maybe more than "a step up" from the curvy copter. Definitely well worth the money in my opinion so far.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 5:42 pm 
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Brandon Enright wrote:
...Both of you are cheating :D You're catching on overhang bandaging. On this Curvy Copter Plus the inner triangles are so small and nearly triangular that the overhang bandaging is very minor. ...
I have thoroughly scrambled and solved it, using fudging turns for sure. polymaker wrote on February 21st above about fudging, so I thought that the turns I used are normal.
It is an interesting question, which turns are considered legal on this puzzle.
Brandon, I recollect a sequence you had shown me for the Curvy Copter more than a year ago and that sequence wasn't possible on the Helicopter Cube. So, it doesn't help much to say that the overhang bandaging on the Unbandaged Helicopter Skewb is more significant and therefore the slightest overhang on the Curvy Copter Plus prohibits a certain turn.

Let's take an example:

Start with the solved state.
Notation: UR+ = clockwise jumbling turn of UR to the next jumbling position
UF- counter clockwise turn to the next jumbling position
Image

After UR+ UF- UR- UF+

Image

Question A: Is UB a legal turn? (On a Curvy Copter I would say Yes.)

Image

The corners touch ever so lightly, still somebody could speak of a slight overhang.

I understand that the green triangle in the F face causes an overhang and FD is not legal and FL is not legal.

FD:
Image

FL:
Image

Indeed, FD and FL can be performed without force similarly easy as UB.

BTW, I'm not yet convinced that the "cheating" makes the puzzle much easier.
The fudging turns can put the puzzle into states that can never be reached without fudging.
So, the scrambling is limited, too, if you avoid carefully any "overhang" turns.
Because the fudging turns can be performed easily, you can reach "illegal" states - illegal as I understand your definition - by accident.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 6:08 pm 
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Konrad, I always love seeing your puzzle photography. You do such a great job of capturing puzzles in their most beautiful state :-)

Konrad wrote:
Brandon, I recollect a sequence you had shown me for the Curvy Copter more than a year ago and that sequence wasn't possible on the Helicopter Cube. So, it doesn't help much to say that the overhang bandaging on the Unbandaged Helicopter Skewb is more significant and therefore the slightest overhang on the Curvy Copter Plus prohibits a certain turn.
Yeah they're definitely different puzzles.

The way I look at it, the "natural geometry" of this puzzle is a Rhombic-Dodecahedral Sphere. The sphere doesn't have any overhang bandaging at all. On the other extreme there is the Unbandaged Helicopter Cube which has tons of overhang bandaging and none of it is ambiguous so you don't have to wonder whether you're doing a legit move or not. The Curvy Copter Plus falls into a ugly grey area where if you're very careful it behaves the same as an Unbandaged Helicopter Cube but if you aren't it's easy to make it behave a bit more like the spherical version of the puzzle.

Konrad wrote:
BTW, I'm not yet convinced that the "cheating" makes the puzzle much easier.
The fudging turns can put the puzzle into states that can never be reached without fudging.
So, the scrambling is limited, too, if you avoid carefully any "overhang" turns.
Because the fudging turns can be performed easily, you can reach "illegal" states - illegal as I understand your definition - by accident.

Yeah difficulty is hard to objectively quantify but there is precedent for adding freedom to a puzzle both increasing the number of states AND decreasing the difficulty of the puzzle. I'm pretty convinced that the overhang bandaging is what makes unjumbling the Unbandaged Helicopter Cube tricky (and very fun!). The more freedom you have the easier it is to move from state to state, even if more states are available.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 6:12 pm 
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Brandon, do you agree with my comments in my last post about what is legal or illegal by your definition:
UB is legal, FD and FL are not?

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Feb 27, 2014 6:17 pm 
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Hello,

I played a little bit around and found some commutators which could help to solve that cube.
I dont know what kind of notation I can use to describe the algorithms. So I just try to explain it.
If somebody comes up with a useful notation for this cube I will try to write it down properly.

1. This pattern you get after 3 eps. But not turning the sides (edges) 180 degree just almost 90 degree.

Attachment:
eps.JPG
eps.JPG [ 42.95 KiB | Viewed 3080 times ]


2. This is the pattern you get after 2 regular jumbling moves (like on the curvey copter)
Jumbling left, Jumbling right

Attachment:
jumble 1.JPG
jumble 1.JPG [ 41.7 KiB | Viewed 3080 times ]




3. Now it gets a little bit more interesting. With this algorithm we seperate the "inner corners" from the "inner edges"
To get this pattern you must turn your front upper edge first by almost 90 degree clockwise.
Then bring your right front edge and your upper left edge in jumbling position (right front edge towards you, upper left edge away from you). Now jumble. Then bring the right front edge and the upper left edge back in its original position. (Your front upper edge is still turned by almost 90 degree clockwise). Now turn the upper front edge by 180 degree counterclockwise and perform the same algorithm on the left side (with the left front edge and the upper right edge). Finally turn your front upper edge back in its original position. (Sounds complicated but gets performed quite fast)

Attachment:
jumble 2.JPG
jumble 2.JPG [ 40.59 KiB | Viewed 3080 times ]



4. This pattern you get if you first perform the "regular jumble move" from 2. and then perform the jumble move from 3.

Attachment:
jumble 3.jpg
jumble 3.jpg [ 46.33 KiB | Viewed 3080 times ]



I hope this can help a little bit to tame that beast :)

Good luck!

Dr. Twist


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Fri Feb 28, 2014 3:40 am 
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Thanks for sharing Dr. Twist!

I had proposed a notation in my post above already:
1. Name the faces as on a Rubik's Cube: U, D, F, B, R, L
2. Name the edges as on a Rubik's cube UF, UR, UL, UB, Df, DR, DL, DB, FL, FR, BL, BR
3. 180° degree turns are named after the turned edges: UF, UR, UL, UB, Df, DR, DL, DB, FL, FR, BL, BR(this is a usual notation)
4. Clock wise turns to the next position, where a jumbling move becomes possible: UF+ etc, counter clockwise turns UF- (I have seen this used by others, but I do not think that it is a common standard)

The EPS for your picture 1 would be UR+ UF- UR- UF+ (that's what I wrote down for my example above)

I do not have time right now, otherwise I would have written your other algorithms in this notation.

For me the hard part was bringing the puzzle back to a cubic shape.

I'm interested, if the others who have solved it, have "cheated" as Darryl and me. (cheat = neglect neglectible overhang bandaging)

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Fri Feb 28, 2014 4:46 pm 
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Hello Konrad,

Konrad wrote:
The EPS for your picture 1 would be UR+ UF- UR- UF+ (that's what I wrote down for my example above)


thank you. Your notation looks very logic and useful to me. How you would write the jumbling move (maybe J and J')?
If somebody would like to use the commutators which I posted I´ll try to write them down using your notation.


Konrad wrote:
For me the hard part was bringing the puzzle back to a cubic shape.


Dito! That was the hardest part for me too (solved it 2 times now). To bring the puzzle back into cubic shape I just used the commutator "UR+ UF- UR- UF+". If you repeat this commutator 6 times the cube is back in the state where you started. => There are 6 states. I analysed how the orientation of the corners changed in each state. With this knowledge I tried to set up the shapeshifted cube in a way that at least one corner gets oriented correctly if I perform the algorithm n times. It is kind of a brute force method and very tedious. I hope somebody will come up with a smarter method soon :-)


Konrad wrote:
I'm interested, if the others who have solved it, have "cheated" as Darryl and me.


Concerning "cheating" I had the feeling that some moves are more"illegal" than others. My rule was that if a turn needs physical force I dont do that turn. In some special cases I was not sure. The cube was kind of hanging. But on the outside there was nothing visible which was blocking. So I didnt know if this is just a sort of "catching" which many puzzles have because some pieces are not properly aligned inside the cube or if it is a illegal move.
But sometimes, if just minimal force is needed I do the turn.

Anyhow I think I will have heaps of fun with that puzzle :-)

Best regards
Dr. Twist


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Fri Feb 28, 2014 4:55 pm 
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Konrad wrote:
Brandon, do you agree with my comments in my last post about what is legal or illegal by your definition:
UB is legal, FD and FL are not?

I wouldn't go so far to call them illegal. I just think all three should be avoided where possible. You have to give yourself some leeway in the solve though because they're just barely bandaged it can sometimes be hard to tell when you did a move that just fudged by.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Fri Feb 28, 2014 5:45 pm 
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I couldn't tell if it was just poorly aligned or if I wasn't supposed to make the turn. I ended up making these turns and I guess I could just say the puzzle is fudged. I'll have to attempt again without making these turns.

-d


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 01, 2014 10:38 am 
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Hi doctor twist and others that might be interested.
I want to elaborate a bit the proposed notation
I'm going to embed some comments below in blue.
doctor twist wrote:
Hello,

I played a little bit around and found some commutators which could help to solve that cube.
I dont know what kind of notation I can use to describe the algorithms. So I just try to explain it.
If somebody comes up with a useful notation for this cube I will try to write it down properly.

1. This pattern you get after 3 eps. But not turning the sides (edges) 180 degree just almost 90 degree.

= (UR+ UF- UR- UF+)x3 = shorthand [UR+, UF-]x3

2. This is the pattern you get after 2 regular jumbling moves (like on the curvey copter)
Jumbling left, Jumbling right

= FR- UL- UF UL+ FR+ UF & FL+ UR+ UF UR- FL- UF

Note: Any turn without a suffix +/- is always an 180 degree turn of an edge, independent of the fact if it is a doctrinaire turn or if the puzzle is in a jumbling position.


3. Now it gets a little bit more interesting. With this algorithm we seperate the "inner corners" from the "inner edges"
To get this pattern you must turn your front upper edge first by almost 90 degree clockwise.
Then bring your right front edge and your upper left edge in jumbling position (right front edge towards you, upper left edge away from you). Now jumble.

UF+ FR- UL- UF
The jumbling turn is a 180 degree turn. Because the setup is completely symmetric, the shape of the puzzle does not change.


Then bring the right front edge and the upper left edge back in its original position. (Your front upper edge is still turned by almost 90 degree clockwise).
FR+ UL+

Now turn the upper front edge by 180 degree counterclockwise
You do not mean 180 degree here, I think, but you want to bring the UF edge into a mirrored position by UF- (inverse of the former UF+) and the mirrored setup UF-
and perform the same algorithm on the left side (with the left front edge and the upper right edge).
FL+ UR+ UF UR- FL-

Finally turn your front upper edge back in its original position. (Sounds complicated but gets performed quite fast)
UF+

....

I hope this can help a little bit to tame that beast :)

Good luck!

Dr. Twist
Personally, I feel that a single swap of two triangles is what we are looking for.
That means that I would use the first part of your sequence only.
We do not care about maintaining edges correctly oriented at that early stage.
While reducing the already cubic shaped puzzle to a Curvy Copter, you can use various symmetric setups where a 180 degree turn swaps just two triangles, creating at least one CC centre at a time.
If you encounter a single flipped edge parity at the very end, you need to setup a swap of two identically looking triangles.

Your setup sequence is nice for swapping triangles on edges in the same orbit.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 01, 2014 4:08 pm 
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Hello Konrad,

thank you so much for your great effort.

Konrad wrote:
You do not mean 180 degree here, I think, but you want to bring the UF edge into a mirrored position by UF- (inverse of the former UF+) and the mirrored setup UF-


Exactely! That was what I meant :-)

Konradl wrote:
Personally, I feel that a single swap of two triangles is what we are looking for.


Do you mean like this?

Attachment:
single triangle swap.jpg
single triangle swap.jpg [ 46.99 KiB | Viewed 2843 times ]


I found out how to create a clean swap of 2 triangular pieces. Nothing else on the cube is swapped or misoriented. (It is completely solved). But I was not able to find an easy algorithm to create that swap I would call it more a procedure.
I´ll try to explain how it works. For complicated parts I try to use your notation :-).

1. Swap to triangular pieces like that:

UR+, UF, UR+, UB, UL, UB, UR-, UF, UR-

As you can see you swapped 2 triangular pieces, but you displaced some other stuff. If you now just turn the wrong flipped middle edge correcty you just need some simple eps to bring everything back in place. Everything? Well, not entirely. Two small outer corners of indomitable permutation still holding out against the solver ;-) In easy words, you will encounter that two outer corners are in place and two must swap.
To avoid this I do the following manoevre:

2. Your goal is to perform the algorithm again then you get rid of the parity. To achieve this you have to set up the cube so, that one triangle which you have swapped before will be exchanged with a triangle of the same color like the other triangle which you swapped before. If you now perform the algorithm again you change 2 triangles of the same color (so you keep the swap) and you get rid of your parity.

3. Solve the cube like a regular curvey copter

Please dont hesitate to ask any question if it is not clear enough.

Good luck :-)


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 01, 2014 4:24 pm 
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doctor twist wrote:
I found out how to create a clean swap of 2 triangular pieces. Nothing else on the cube is swapped or misoriented. (It is completely solved).
I'm pretty sure a pure swap isn't possible. I think your procedure must make use of the fact that there are duplicate inner small triangles.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 01, 2014 6:18 pm 
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Brandon Enright wrote:
doctor twist wrote:
I found out how to create a clean swap of 2 triangular pieces. Nothing else on the cube is swapped or misoriented. (It is completely solved).
I'm pretty sure a pure swap isn't possible. I think your procedure must make use of the fact that there are duplicate inner small triangles.


Yes, that is true. I use duplicate pieces. I guess I did not correctly understand what the definition of a "clean" swap is.
So please apologise if I used the wrong terminology.

Just for better understanding I´d like to ask you a question.

Lets take a regular 4x4x4 cube and perform the following algorithm: u2, R2, F2, u2, U2, F2, R2, u2

The result is: I swapped 2 wedges.

Is this a clean swap?
I ask this, because if I am performing the same alg on a 4x4x4 supercube. I get the same result concerning the wedges, but additionally I can obsever that the right center rotated bei 180 degree.


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 01, 2014 11:09 pm 
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doctor twist wrote:
Yes, that is true. I use duplicate pieces. I guess I did not correctly understand what the definition of a "clean" swap is.
So please apologise if I used the wrong terminology.
Well, I equated "clean" with "pure" which is the term we normally use for things without side effects.

doctor twist wrote:
Just for better understanding I´d like to ask you a question.

Lets take a regular 4x4x4 cube and perform the following algorithm: u2, R2, F2, u2, U2, F2, R2, u2

The result is: I swapped 2 wedges.
Can you check your sequence notation? When I do it I get a bit of a mess. Plenty of stuff moves.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Mar 02, 2014 3:32 am 
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It is a problem of notation: Dr. twist's u2 turns two layers, the U layer and the slice layer beneath it.
This is SIGN notation.

That's why I always feel that notation needs a reference.
Most people see "u" as the (old) WCA notation of a slice turn below U.

In my opinion it swaps two 3x3x3 edges (4 4x4x4 edges) clean on an ordinary 4x4x4, but certainly not on a 4x4x4 Super Cube.
It is, however a matter of definition, what "clean" means.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Mar 02, 2014 9:36 am 
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Brandon Enright wrote:
Well, I equated "clean" with "pure" which is the term we normally use for things without side effects.


With this definition I could maybe say, that a swap of to triangular pieces is possible because I cant see any sideeffects. On the other hand it is no real swap. In fact it is a three cycle and because we use 2 pieces with the same color it´s invisible. If I would mark the 3 pieces which I use it would be clear.

Brandon Enright wrote:
Can you check your sequence notation? When I do it I get a bit of a mess. Plenty of stuff moves


Please excuse me if my notation was confusing.
With "u" I meant turning both upper layers (like Konrad said)
Btw, I saw many different notations meaning exactely the same thing. In this case for example: 2Uu, 2u, Uw2, even 2Uw2

Konrad wrote:
That's why I always feel that notation needs a reference.


Is there any standard notation which we should use here?
I messed up my puzzles so many times, because I misunderstood a kind of notation :-)

Best regards


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Mar 02, 2014 2:51 pm 
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doctor twist wrote:
...
Konrad wrote:
That's why I always feel that notation needs a reference.
Is there any standard notation which we should use here?
I messed up my puzzles so many times, because I misunderstood a kind of notation :-)

Best regards
Yeah, especially the lower case "u" can interpreted in different ways. I remember that I had confused you by the "u+" in a different thread :oops:
I think any notation is OK, as long as you make a reference, like SIGN Notation or explicitly what you mean.
Personally, I use WCA notation and we discussed it here Slice moves in WCA notation.

Regarding the FT dodecahedron we have discussed a TP standard and you can look at the results here.

Now, let us go back to the Curvy Copter Plus: :)
Whenever you swap just a single pair of triangles, an edge will be flipped as well. This is a visible side effect.
You need to swap in addition two identically looking triangles flipping it back.
So, we agree that we have not a pure single swap, but a two-two swap (two pairs are swapped) - or a 3-cycle.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Mon Mar 03, 2014 11:19 pm 
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Does anyone have tips on disassembling the Curvy Copter Plus? I have managed to completely lock up my puzzle by "pushing through" overhang bandaging too many times during my first scramble. Nothing will turn anymore because 14 out of the 24 triangles are oriented incorrectly. There is so much catching that it's just unplayable. I need to just take it apart and start over.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 04, 2014 12:00 am 
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It's actually fairly easy to take apart and put back together. To take it apart, turn one of the sides to roughly the point where you can jumble and just pull on one of the fish eyes until it comes out. Then repeat and it should all just fall apart eventually. Putting back together is pretty straight forward, when you get to the last few pieces, you want to kind of pull everything away from the fish eye you are putting back in. Once it's in, let go and line everything up.
I hope this make sense.

-d


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 04, 2014 9:34 am 
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darryl wrote:
It's actually fairly easy to take apart and put back together. To take it apart, turn one of the sides to roughly the point where you can jumble and just pull on one of the fish eyes until it comes out. Then repeat and it should all just fall apart eventually. Putting back together is pretty straight forward, when you get to the last few pieces, you want to kind of pull everything away from the fish eye you are putting back in. Once it's in, let go and line everything up.
I hope this make sense.

-d

Thanks, Darryl. That certainly helped. Assembly was no problem, but finding a turn with enough give to allow me to pull out the triangle was no easy task. I really jacked this thing up, didn't I? Haha

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 11, 2014 1:06 am 
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I got my copy today :D I gave it a solve and realized that the overhang bandaging is not actually what should be blocking moves. That is, when you have a inner triangle twisted, it actually has part of its mechanism inside of the puzzle jutting into the path of an adjacent face. On a Bandaged Helicopter Cube the overhang prevents you from doing the move. It turns out though that even if the overhang bandaging weren't there, the move would still be illegal because of the internal mechanism jutting into the path of the adjacent face. In this case the overhang bandaging is helping you see a move that is blocked.

Also, I found a nice sequence for swapping a pair of inner-triangles with the outer trapezoidal parts in the reduction-pairing phase. It's as [3:1] conjugate where all of the moves are jumbling moves (although the 1 is actually a 180 degree turn from a partial-turn state to another partial-turn state).

Fun puzzle! Too bad it allows you to push through to illegal positions which cause a lot of jamming.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 11, 2014 5:30 am 
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Brandon Enright wrote:
...
Also, I found a nice sequence for swapping a pair of inner-triangles with the outer trapezoidal parts in the reduction-pairing phase. It's as [3:1] conjugate where all of the moves are jumbling moves (although the 1 is actually a 180 degree turn from a partial-turn state to another partial-turn state).

Fun puzzle! Too bad it allows you to push through to illegal positions which cause a lot of jamming.
Now I hope for a video :D I know, I know, that there are many other things on your agenda. :roll: :)

Regarding your swapping sequence: Is it by accident the same (or similar to) the one shown by doctor twist in the first part of his algorithm "3." above?
UF+ FR- UL- UF UL+ FR+ UF- = [UF+ FR- UL- : UF]
This swaps two triangles between Curvy Copter centres in the same orbit, i.e. they are after the sequence paired with different trapezoidal pieces.
If the CC centres are in different orbits I use sequences like FR- UF FR- FD FL FD FR+ UF FR+ = [4:1]

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 11, 2014 10:07 am 
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Konrad wrote:
Brandon Enright wrote:
...
Also, I found a nice sequence for swapping a pair of inner-triangles with the outer trapezoidal parts in the reduction-pairing phase. It's as [3:1] conjugate where all of the moves are jumbling moves (although the 1 is actually a 180 degree turn from a partial-turn state to another partial-turn state).
Regarding your swapping sequence: Is it by accident the same (or similar to) the one shown by doctor twist in the first part of his algorithm "3." above?
UF+ FR- UL- UF UL+ FR+ UF- = [UF+ FR- UL- : UF]
This swaps two triangles between Curvy Copter centres in the same orbit, i.e. they are after the sequence paired with different trapezoidal pieces.

Indeed it is. I suppose it is rather obvious so I'm not surprised I found the same one.

Konrad wrote:
If the CC centres are in different orbits I use sequences like FR- UF FR- FD FL FD FR+ UF FR+ = [4:1]
I hadn't considered trying to find another one that worked on a set not in the same orbit. I'll have to look for another sequence before I try this one out :-)

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 11, 2014 10:12 am 
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For the unjumbling stage, when you have an inner-triangle twisted out of place like this:
Image

How do you twist the corner and triangle? I use a 16-move sequence that's [A,B]x2 [C,D]x2 where after a cube rotation about a corner A -> C and B -> D. I figure there is probably something shorter and more direct but memorizing something that's basically 2 moves repeated and the rotate the cube and then the same 2 moves repeated is just too easy to ignore.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Tue Mar 11, 2014 12:40 pm 
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Brandon Enright wrote:
I use a 16-move sequence that's [A,B]x2 [C,D]x2 where after a cube rotation about a corner A -> C and B -> D. I figure there is probably something shorter and more direct but memorizing something that's basically 2 moves repeated and the rotate the cube and then the same 2 moves repeated is just too easy to ignore.


I agree. This is basically how I align all the triangles.

As for the illegal moves - I hope no one calls the cops on me since I know ignorance is not a defense :)

-d


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Wed Mar 12, 2014 2:19 am 
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Brandon Enright wrote:
How do you twist the corner and triangle?
Also, Konrad, do you have a sequence to perform this pure? I was laying in bed unable to sleep thinking about operations on this puzzle and I came up with one. It's a lot of moves but it's very simple in concept. Most of the moves are because the overhang bandaging requires some messiness that wouldn't be required on the spherical version of the puzzle.

Also, a video will be coming as soon as I can :D Do you have anything specific you'd like me to cover? I don't think I have a short, concise, fool-proof strategy for unjumbling the puzzle. There is too much situational-based intuition to describe it fully in a way that will make sense to everyone.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Wed Mar 12, 2014 6:12 am 
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Brandon,

when I made the picture you quoted above, I was not aware of the overhang bandaging issue.
So, I used a (probably well known) sequence for the Helicopter Cube to turn two corners pure and did
[[UR+, UF-]:[y (UR UL UB UR UL UF)x2 y'] I'm sure that at least one turn is considered illegal :wink:
For reduction purposes I use a very simple idea: I replace a corner by a triangle, twist this "corner triangle" using 180° turns, leaving the surrounding pieces in place and inverse the first [1,1]. It is a [4:11] and 3 turns more than your 16 move sequence.

Regarding the video, I have no specific suggestions.
I have not scrambled the puzzle again since I'm aware of the overhang bandaging issues. I think you need to scramble it carefully, because if you scramble it using illegal moves you are probably in a state that needs illegal moves for solving. I think it is bad that the puzzles allows "illegal" turns in the first place.
Is it any better in the Shapeways version?

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Thu Mar 13, 2014 10:06 pm 
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I figured out why there is internal bandaging on the Curvy Copter Plus even when it looks like there shouldn't be.

When we think about a Curvy Copter Plus, we think about a puzzle with cuts like the following:
Attachment:
ideal_cc_plus.png
ideal_cc_plus.png [ 29.09 KiB | Viewed 2213 times ]

The blue cuts are the unbandaged cuts.

But that's not how a real physical puzzle works. A puzzle with mechanism on the pieces needs to have the mechanism portion of pieces be a deeper cut than that. Like this:
Attachment:
real_cc_plus.png
real_cc_plus.png [ 30.89 KiB | Viewed 2213 times ]

Notice how the inner triangle piece no longer has a triangular mechanism? It turns into a chevron shape and a new set of pieces are created but left out of the design (shown in pink). Because the mechanism on the inner triangle pieces with the chevron mechanism is no longer rotationally symmetrical, if you twist one it will stick out into the pink region. This will cause collisions with adjacent moves. The same is true if you put a corner in the place of an inner triangle.

You can see that this is true on the physical pieces:
Attachment:
cc_plus_wedge_group_mech.png
cc_plus_wedge_group_mech.png [ 393.66 KiB | Viewed 2213 times ]


You can see this jutting out when you twist a triangle in place shown here as the highlighted red piece:
Attachment:
cc_plus_triangle_twisted.png
cc_plus_triangle_twisted.png [ 2.51 MiB | Viewed 2213 times ]

If you try to turn the edge closest to the camera that has the pieces removed, it will collide with the mechanism sticking out from the twisted red triangle.

So even the spherical version of this puzzle with no overhang bandaging has forbidden moves internally. Only the ideal mechanism-less spherical version would allow these moves.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sat Mar 15, 2014 4:49 pm 
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Brandon Enright wrote:
So even the spherical version of this puzzle with no overhang bandaging has forbidden moves internally. Only the ideal mechanism-less spherical version would allow these moves.
So if we gently separate the pieces and and coax the edge through a turn:

a) It won't hurt the puzzle mechanism in any way; and
b) Should be considered a legitimate turn

What is the consensus?

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Apr 06, 2014 6:05 am 
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Hi friends,

is it possible, than one outer center is flipped ?
One outer-center popped out. After reinserting (wrong of two possibilities)the puzzle was unsolveable.

Is it possible to turn the puzzle "safe" after more than 3 or 4 inner-centers are turned ?
There are possible turns because the tension. But geometric the turning must be forbidden.

Cheers,
Andrea


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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Apr 06, 2014 10:43 am 
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Andrea wrote:
Hi friends,

is it possible, than one outer center is flipped ?
One outer-center popped out. After reinserting (wrong of two possibilities)the puzzle was unsolveable.
I'm pretty sure that they can be flipped in pairs only, I cannot proove it mathematically, though.
Andrea wrote:
Is it possible to turn the puzzle "safe" after more than 3 or 4 inner-centers are turned ?
There are possible turns because the tension. But geometric the turning must be forbidden.

Cheers,
Andrea
One drawback of the puzlle is the fact, that you can do a lot of moves "physically" that have to be considered illegal from a puristic point of view. If you avoid "illegal" turns during scrambling not many triangles (= inner centres) can be twisted (= not flat on the cubic shape) at a time.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Apr 06, 2014 12:32 pm 
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Brandon Enright wrote:
So even the spherical version of this puzzle with no overhang bandaging has forbidden moves internally. Only the ideal mechanism-less spherical version would allow these moves.

Technically speaking, if one were to make the mechanism groove shallower cut rather than deeper cut, then the puzzle would also be able to make these turns. Also, if one simply made the cuts on this puzzle spherical then there would be no overhang bandaging at all.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Apr 06, 2014 1:13 pm 
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benpuzzles wrote:
Technically speaking, if one were to make the mechanism groove shallower cut rather than deeper cut, then the puzzle would also be able to make these turns.
Is it physically possible to make a puzzle that will hole together where the mechanism is shallower than the external cuts?

benpuzzles wrote:
Also, if one simply made the cuts on this puzzle spherical then there would be no overhang bandaging at all.
I'm not sure what you mean. Do you mean the external shape of the puzzle spherical? I was calling the internal bandaging due to the mechanism "overhang" bandaging even though you can't see any overhang at the surface.

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 Post subject: Re: How to solve the Mefferts Curvy Copter Plus?
PostPosted: Sun Apr 06, 2014 1:57 pm 
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Brandon Enright wrote:
benpuzzles wrote:
Technically speaking, if one were to make the mechanism groove shallower cut rather than deeper cut, then the puzzle would also be able to make these turns.

Is it physically possible to make a puzzle that will hole together where the mechanism is shallower than the external cuts?

I'm pretty sure it's possible, as long as you make the grooves large enough.
Brandon Enright wrote:
benpuzzles wrote:
Also, if one simply made the cuts on this puzzle spherical then there would be no overhang bandaging at all.
I'm not sure what you mean. Do you mean the external shape of the puzzle spherical? I was calling the internal bandaging due to the mechanism "overhang" bandaging even though you can't see any overhang at the surface.

What I mean is to make the cuts themselves spherical. This in effect would make them look a bit more curvy on the puzzle, but as a result this curvature would make the pieces shaped in such a way that they don't cause overhang bandaging.

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