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 Post subject: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:30 pm 
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The Curvy Copter plus is a Curvy Copter puzzle but slightly unbandaged so more moves are possible. It is similar to the Crazy Comet puzzle by Oskar van Deventer.

The Curvy Copter plus is the same size as a regular Curvy Copter puzzle:
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File comment: Comparison picture of the Curvy Copter plus puzzle with the regular Curvy Copter
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When jumbling the normal Curvy Copter you are quite constrained. Not only does the unbandaging of the Curvy Copter plus produce an even more interesting and beautiful face pattern, it also makes the jumbling feel less constrained. Solving wise I'm not sure yet, but it will make some interesting shapes.

This is one of the rotations that is enabled by the unbandaging:
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File comment: One of the special moves the Curvy Copter plus puzzle can perform.
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Unfortunately, Shapeways polygon limit prevents me from offering this puzzle on my Shapeways puzzle shop. Time allowing, I will try to find a solution for this. However, you can contact me directly to order a DIY kit for $160/€135 or a completed puzzle for $230/€165.

Of course, you will be able to try this puzzle and any of my other puzzles like the Dino Skewb, Helicopter Skewb, Constrained Cube and Tetrahedral Twins at the Dutch Cube Day 2010.

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Last edited by TomZ on Sun Oct 10, 2010 4:01 pm, edited 1 time in total.

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:42 pm 
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Why don't you just put it on Shapeways in two halves? It would only cost $1.50 more.

Anyway, awesome puzzle! I enjoyed looking at it yesterday :)

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:49 pm 
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That's actually not quite true. It would cost $16.5 more (undocumented part of the pricing model). But any way, even two halves don't suffice (the model has lots of curved surfaces which take up loads of space).

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:52 pm 
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This is a beautiful puzzle, Tom. I hope to own one of these one day. Oh, and by the way, on your website, paragraphs two and three basically say the same thing word for word.

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Last edited by Luke on Sun Oct 10, 2010 4:13 pm, edited 1 time in total.

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:54 pm 
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wow! cool puzzle you got there! :) maybe I should get this one instead of the curvey copter?

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 3:59 pm 
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Really great puzzle Tom. Can this be viewed as a cubic version of Oskar's crazy comet? also, do you ever plan on making a non curvy version?

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 4:17 pm 
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That is one beautiful puzzle! I don't usually buy other people's custom puzzles, but I might have to make an exception with this one! Well done as usual, Tom.

-π (Eitan)

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 6:09 pm 
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Amazing puzzle!!!

2 questions
-does this fully unbandage the puzzle?
-could the same be done on other edge turning cubes such as the 24 cube or your curvy copter 2?

(I know a jumbling puzzle can't be truely unbandaged but when solved the extra pieces are bandaged in place)

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 6:58 pm 
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Both amazing and beautiful TomZ. My mind is literally blown. Great work.

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 9:10 pm 
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TomZ wrote:
The Curvy Copter plus is a Curvy Copter puzzle but slightly unbandaged so more moves are possible.
TomZ is the basically the same idea you mentioned here? Is so I'm glad to see that idea wasn't dropped. If this is a different partial unbandageing could you explain the difference?

GREAT PUZZLE!!!
Carl

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 Post subject: Re: Curvy Copter plus
PostPosted: Sun Oct 10, 2010 9:16 pm 
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Absolutely my favorite design from you Tomz, really a very impressive puzzle, If I were to buy a puzzle I could never sole it would be this one. :lol:


It makes me wonder if you built a 24 cube with the layer mechanism with this copter cube if some of the internal blocking would dissipate.


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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 12:25 am 
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Yes!!!! I am so excited to see this puzzle!! I also started to design a puzzle with the same idea, but using a regular helicopter cube instead of TomZ's curvy version. I very quickly realized it would turn out quite ugly and not work in any practical fashion so I dropped it to move onto something else. I never even thought of using curved cutting planes!! Excellent job TomZ!!!!!!! :mrgreen: :mrgreen:

If anyone remembers my conversation about the "freedom cuts" on Oskar's Meteor Madness puzzle on the More Madness puzzle thread. The Curvy Copter Plus is EXACTLY what a curvy copter would like if it were "freedom unbandaged" (clearly, I need to come up with a better term for this... :lol: any suggestions?) Btw, the picture from the post I linked above is incorrect. As Oskar correctly pointed out later in that thread there are several bandages I missed. I have yet to take a second stab at it.

Now what does this mean for the puzzle? Solving will be WAY different. Assuming TomZ's design doesn't produce any overhang bandaging situations (quite a big assumption for now). This puzzle will feel much less like a traditional twisty puzzle with coincidental jumbling moves and more like a jumbling puzzle (OSKAR STYLE!!!) with coincidental non-jumbling moves. I would actually LOVE to play this thing, as it would do some bizzare things. For example: for all practical purposes, the corner pieces and the new small triangle pieces can be considered mathematically identical, just like 2 different corners on a 3x3x3 (or more accurately a corner and a center of a mastermorphix; 2 pieces that look different but are mathematically/mechanically identical), and switching pairs of them will have no mathematical consequence on the rest of the puzzle. Suddenly the idea of the "natural shape" of this puzzle becomes much more complicated. And jumbling will no longer feel like a maze, but much more of a natural extension of the available moves (if you've ever played with the jumbling moves of a helicopter cube you'll know what I mean, so many moves are blocked that most of the time there's really only one thing to do and that always gets you close to getting the puzzle back in shape, so save for a few exceptional cases, getting a helicopter cube back in shape after jumbling really isn't that difficult. WELL NO MORE FOR THIS PUZZLE!!)

:lol: I find this puzzle SO exciting, I just thought of another ramification of this design. It would not only be possibly but likely easier to solve this puzzle NOT by shape first, but by first placing the edges of the cube, then the rectangular shaped pieces all without regard to the shape of the puzzle. The remaining corners and triangular pieces, some of which can and most likely will be in eachothers' locations by now would be solved last at the same time. How awesome would it look to solve a Helicopter cube without getting it into cube shape until the very last move?!?!?

DOES WANT 8-)

Peace,
Matt Galla

PS Probably the easiest (not necessarily best) way of thinking about this is that this jumbling puzzle has been completely unbandaged to a certain point. That point is the maximum number of bandages that can be broken such that all unbandaged pieces can be spearated and the "primary" pieces (the edges) are not cut in any way from the default cut pattern. I'm defining primary pieces to be any piece that attaches directly to the core of the puzzle. By this same definition, Fairly Twisted, Asteroid Attack, Meteor Madness, and probably some others I'm forgetting are all not default jumbling puzzles but jumbling puzzles that have been unbandaged up to the primary pieces.


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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 1:26 am 
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Very cool. It's really hard to tell what the cuts do without watching the video. I've been wanting to see and "unbandaged" helicopter cube for a while. I tried making a sketch but I think in unbandaged it in a different way. Excellent work TomZ.
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Last edited by GuiltyBystander on Mon Oct 11, 2010 10:23 am, edited 1 time in total.

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 4:06 am 
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Good job! :wink: It's too crazy to believe.


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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 4:54 am 
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Its a very nice puzzle :D Now wheres the money when you need it... :lol: Does the clicking mechanism help keep the cube intact?

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 5:07 am 
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Very nice puzzle! Just a bit to late for becoming number four in my Christmas parcel :lol:
(The Compy Skewb, Curvy Copter II and Helicopter Skewb have arrived safely and are put away until Christmas :D )
Now it is on my wishlist!

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 7:15 am 
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Allagem wrote:
PS Probably the easiest (not necessarily best) way of thinking about this is that this jumbling puzzle has been completely unbandaged to a certain point. That point is the maximum number of bandages that can be broken such that all unbandaged pieces can be spearated and the "primary" pieces (the edges) are not cut in any way from the default cut pattern.
Does talking about the order of the unbandaging make sense? First order unbandaging... Second order unbandaging... etc?
GuiltyBystander wrote:
I tried making a sketch but I think in unbandaged it in a different way.
Ok... what is this then? Maybe a thread about the theory/methods of partially unbandaging jumbleable puzzles should be started... though I'm at a loss on this one. How many different ways are there to take a "first pass" at unbandaging a Helicopter Cube?

And the curvy cuts are making it hard for me to see what's going on here... what would this look like if it were a Helicopter Plus?

Carl

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 8:11 am 
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I took one look and said "Oh sneeze."

Are there any color-variant shape-invariant positions?

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 8:20 am 
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Can the rectangle pieces between the corners and central triangles rotate 180 degrees? This really is an amazing puzzle!

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 12:21 pm 
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wwwmwww wrote:
Does talking about the order of the unbandaging make sense? First order unbandaging... Second order unbandaging... etc?

Absolutely! Although I don't think order is a good word to describe it. There is an infinite list of cuts you can make on jumbling puzzles such as the Helicopter Cube. While some of these cuts require the existence of others, there is no "correct" sequence and you have several choices about which cut to make next. So while it does make sense to only do some of these cuts, it can't be completely defined by just a number :wink:
wwwmwww wrote:
How many different ways are there to take a "first pass" at unbandaging a Helicopter Cube?

ALOT. Especially if you don't require that the cuts be symmetrical over the whole puzzle. Go ahead. Try mapping out a few. And actually how do you define the "end" of the first pass?
wwwmwww wrote:
And the curvy cuts are making it hard for me to see what's going on here... what would this look like if it were a Helicopter Plus?

You know this topic made me try to recreate what I briefly worked on a long time ago only to discover that I did it completely wrong the first time. You can indeed make a helicopter cube plus. It looks EXACTLY like a normal helicopter cube. From the outside :wink: All of the triangular pieces have an extra cut that is not visible from the outside while the puzzle is in cube shape (well ok because of some slight rounding of the pieces it might be slightly visible). These cuts run exactly down the hypotenuse of each center triangle piece of a normal helicopter cube and cut the triangle piece roughly in half. So the rectangle pieces from the curvy copter plus are not visible on the helicopter plus (at least not when it is in cubic shape). The visible center triangle pieces on a helicopter plus then would be equivalent to the small center triangles on the curvy copter plus. There would also definitely still be some overhang bandaging so, assuming there is no overhang bandaging on the curvy copter plus (I haven't checked yet), the two puzzles would still be slightly different as some moves will be blocked by overhang bandaging on the helicopter plus but not on the curvy copter plus.

And yes this is exactly the idea TomZ had in this thread (same one Carl linked above), though I must admit at the time I didn't understand. Look at the pictures he provided there and read my explanation above and I'm sure you'll see exactly how a helicopter plus would work :wink:

Gotta go, I got class! :lol:

Peace,
Matt Galla


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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 2:58 pm 
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That's pretty amazing :D, but very confusing. :?

Alex

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 4:04 pm 
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wwwmwww wrote:
GuiltyBystander wrote:
I tried making a sketch but I think in unbandaged it in a different way.
Ok... what is this then? Maybe a thread about the theory/methods of partially unbandaging jumbleable puzzles should be started... though I'm at a loss on this one. How many different ways are there to take a "first pass" at unbandaging a Helicopter Cube?

And the curvy cuts are making it hard for me to see what's going on here... what would this look like if it were a Helicopter Plus?
I've watch the video again a few time and I'm starting to think that maybe they are nearly the same, at least from the outside. The red pieces on mine must disappear when you use curved cuts. You're right, the curvy cuts make it hard to tell what's happening. The curved cuts bring some pieces to the surface like the edge pieces and push others out of existence.

I would not call this a first order unbandaged curvy copter. Here's a bandaged move I see that should be unbandaged for it to be first order because this is the first time a bandage restricts your movements (I think).
1. Jumble UR CW.
2. FR is bandaged.

Hmm. Cancel my earlier statements about my sketch. I'm trying to render the 2 moves above on my cheap attempt and I'm realizing that I missed some cuts too. Actually, I don't know what I did to get what I have now. It's been a while since I did this. So confused...

There was a thread started a while back about jumbling/bandaging order. It didn't go very far though. Jumbling Puzzle Order

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 4:33 pm 
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A very interesting concept, and a brilliant execution. I feel proud to live in the country of the two masters of jumbling, Tom and Oskar. Who needs Ernö Rubik and Uwe Meffert at the DCD when we have the two of you?!

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 6:53 pm 
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This puzzle is simply brilliant. I believe that when solved, it looks even more elegant than Oskar's Crazy Comet, although with the Crazy Comet, every interchangeable piece has the same shape. Are the inner corners perfectly triangular? (meaning if you twist it through 1/3 rotation, it still lays flat on the square surface). The natural way to solve a Crazy Comet/Curvy copter Plus, is to match the center triangles to their respective edges, then the cube can be solved like a normal "Jumbled" Helicopter Cube. But wait, there's more than meets the eye here: if one or more of the center triangles is inadvertently rotated in place, then the twirl parity of the outer corners, which are interchangeable with the inner corners, could become messed up.

It's a shame that my puzzle fund is officially broke now, or I would snatch one of these up in a heartbeat! :mrgreen:

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 9:07 pm 
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Beautiful Puzzle

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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 11, 2010 11:20 pm 
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GuiltyBystander wrote:
I would not call this a first order unbandaged curvy copter. Here's a bandaged move I see that should be unbandaged for it to be first order because this is the first time a bandage restricts your movements (I think).
1. Jumble UR CW.
2. FR is bandaged.


That's right. But notice one of the pieces blocking this particular move (although there are others) is the edge piece, or what I called a primary piece: a piece connected directly to the core of the puzzle (also the type of piece that can only be moved by one rotation and only in orientation, if you need a better definition). *The rule for this puzzle is if a move is blocked it is blocked by a primary piece. The contrapositive is also of course true: if a primary piece does not block a rotation, that rotation is available. The cuts on the curvy copter plus are the minimum cuts needed for those statements to hold true.* This is ONE very natural way of unbandaging a jumble puzzle.

However, you could also unbandage in such a way that the first 2 moves are always available (I'm assuming that is what you would require of a puzzle before it is called a "first order unbandaged" jumbling puzzle). This is also ONE very natural way of unbandaging a jumble puzzle. As your example clearly shows, these two natural "unbandagings" do not result in the same puzzle though they each have a profound impact on the resulting puzzle. (In my opinion the unbandaging style shown here is more significant, but that's just me). This is exactly why I don't think we should have a set way of unbandaging a jumble puzzle or call it specific orders.

Perhaps we COULD have specific rules and names for different unbandaging styles (as it is easily possible to come up with sets of rules of unbandaging that can be generalized to any jumbling puzzle). In which case I hereby dub the 1st style I described above in **'s (present on Curvy Copter Plus and several Oskar puzzles like Fairly Twisted, Meteor Madness, and Asteroid Attack) as Liberty Unbandaging. 8-) (purely because jumbling puzzles cut in this way are "free" to move like a normal puzzle...in the sense that returning each primary piece to its original orientation is always trivial. Jumbling puzzles with these cuts feel much less like a maze than it would without these cuts. If you don't believe me buy one of the above mentioned Oskar puzzles and simulate it both with the liberty unbandagings and without them. You'll see what I mean :wink: ). Do we like the idea of labelling specific unbandaging styles? If so, we should probably start a new thread. I'm feeling guilty about hijacking this one already... :? Sorry TomZ, but your puzzle is just so EXCITING!!! :P

Peace,
Matt Galla


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 Post subject: Re: Curvy Copter plus
PostPosted: Mon Oct 18, 2010 12:28 am 
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Master-Puzzle!!!

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