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 Post subject: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 9:11 am 
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Hey folks,

Today I'd like to present my latest puzzle, the Curvy Copter Skewb.



VIDEO

As you might be able to guess from the name of the puzzle, it is a hybrid puzzle, combining the turns of both the Curvy Copter and the Skewb.



As well as being able to scramble like any regular doctrinaire hybrid puzzle, the geometry of the puzzle allows for very interesting jumbling. For example, once you've turned a Curvy Copter edge by the jumbling angle (about 70.53 degrees), you can then turn around a Skewb corner. Alternatively, you can do a Skewb turn, and half way through that turn you can proceed to do Curvy Copter turns. By combining both Skewb and Curvy Copter turns whilst jumbling, the puzzle can result in some very interesting states.



Another feature that allows even more jumbling moves on the puzzle is the curvature of the Curvy Copter cuts. It is the minimal amount of curvature to be able to turn two adjacent axes on the same slice without it being a forced/illegal turn. Whilst this is possible to do on the normal Curvy Copter, pieces are pushed out and it can become rather difficult to turn. On this puzzle those moves are fine, and so you can do moves like this.



Because I enjoy this puzzle so much, I will be keeping this copy for myself. That means that this will be going up on Shapeways, probably within the next week or so. Prices will start from $130.

VIDEO

Hope you enjoy the puzzle!

Luke :)

(I will add the scrambled and jumbled pictures of the puzzle later, as well as re-edit some of the ones here. The editing is a pain in the neck to do).

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 9:27 am 
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Wow the combination of cuts from the two puzzles looks beautiful. You're designing some really good stuff Luke, well done :)

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 9:28 am 
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Wow! That is so crazy! Good luck solving it. I don't know if you noticed, but it actually seems a lot like Greg's Helimate in some of the ways it jumbles.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 10:10 am 
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Amazing crazy! Beautiful puzzle, it looks real scary when it is fully scrambled. Is the mechanism too complex to be mass-produced?

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 10:12 am 
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I remember you showing this to me a few weeks back without stickers. I couldn't really get a good look at it, but I think you remember my reaction- WOW!
I can't wait for the other puzzle :D :D :D :D

-Doug

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 10:22 am 
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What a beauty. Great job Luke! Hybrids are so much fun to solve.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 10:26 am 
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Another beautiful looking puzzle Luke, that looks like a lot of fun to solve. Awesome.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 11:19 am 
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That one looks so pretty, and the jumbling looks like so much fun, even less unrestricted than in TomZ's Helicopter Skewb! <3

Just one question: why didn't you split the curvy copter face pieces, à la Curvy Copter Plus? Would too tiny pieces have resulted?

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 11:39 am 
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A very beautiful puzzle! Luke, you have designed very impressive puzzles recently!
I fell in love with Tom's Curvy Copter when I saw it in the first place.
This hybrid is even more impressive.
If I remember correctly (I think it was a post of bhearn), a completely jumbled Helicopter Skewb cannot be unjumbled using currently known methods.
OK, I found this viewtopic.php?f=15&t=18695&p=263389&hilit=+helicopter+skewb#p263389

Is it the same here?

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 11:42 am 
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Wow, that's beautiful!

-Eitan

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 11:47 am 
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Gus wrote:
Is the mechanism too complex to be mass-produced?

In my opinion, I would say the mechanism would be ever so slightly more difficult to mass produce than the DaYan Gem IV. Perhaps in a couple of years we'll see puzzles with mechanisms like this being mass produced.

Coaster1235 wrote:
Just one question: why didn't you split the curvy copter face pieces, à la Curvy Copter Plus? Would too tiny pieces have resulted?

Two reasons: Firstly, I wanted a puzzle which could be fully scrambled without being jumbled. On an unbandaged version, one would have to jumble it to make use of the stored cuts. Secondly, I have plans for a series. :)

Konrad wrote:
If I remember correctly (I think it was a post of bhearn), a completely jumbled Helicopter Skewb cannot be unjumbled using currently known methods. OK, I found this http://www.twistypuzzles.com/forum/view ... wb#p263389

Is it the same here?

The problem with the Helicopter Skewb is that you cannot tell what the shapes of the Curvy Copter axes are (either they are rhombuses or they are trapezoids), and so it requires a lot of trial and error to unjumble the puzzle. I have solved the Curvy Copter Skewb, and I can tell you the jumbling is the easy part of it. You have the advantage of being able to see the shapes of the Curvy Copter axes, and can deal with them rather quickly.

Thanks for all the compliments guys! :)

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3x3x3 single: 5.73 seconds.
3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

Buy the Curvy Copter Skewb, NovaMinx, and more here!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 11:54 am 
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I am looking forward to receiving my Copter 3x3 from will_57 next week...
...and then this comes out! It's like London buses :lol:
Straight to the top of my buying list. Wonderful puzzle, that will compliment the Copter very nicely.
Well done.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 12:03 pm 
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Konrad wrote:
If I remember correctly (I think it was a post of bhearn), a completely jumbled Helicopter Skewb cannot be unjumbled using currently known methods.
OK, I found this http://www.twistypuzzles.com/forum/view ... wb#p263389

Is it the same here?

TomZ has his Helicopter Cube + Skewb which mechanically is identical to this puzzle but the Curvy Copter edges and the extra sliced-off part of the Helicopter Cube triangles are both hidden. The jumbling is the same though. The internal edges jumble, you just can't see them.

It is true that you can't use just unjumbling knowledge from the Helicopter Cube to unjumble the Helicopter Skewb (you need a few more tricks) but in general, it isn't that hard. Luk's Curvy Copter Skewb will be slightly easier to unjumble because you can see the configuration of a jumbled edge without needing to infer it.

For solving once unjumbled, the Curvy Copter Skewb will offer more challenge because there are more pieces stickered and many can only be cycled with a mix of both type of cuts.

I have a copy of:
  • TomZ's Helicopter Skewb
  • TomZ's Unbandaged Helicopter Skewb
  • Eric Vergo's Unbandaged Helicopter Cube

Their jumbling is all quite similar. The strategy for unjumbling them is roughly the same even if the specific moves available at any given situation are different. At first they all seem really hard but once you get a feel for the puzzle unjumbling them is pretty fast and easy. Sometimes I run into a trickier situation and have to think but usually I unjumble them in 5 minutes or less.

The advantage to the Curvy Copter Skewb is that it offers more solving challenge once unjumbled (and it looks beautiful!).

Also, for what it's worth, TomZ's CC II unjumbles the same as a Helicopter Cube. Eitan's Master Helicopter and Curvy Copter cubes offer a somewhat different (and pretty fun) unjumbling experience due to the slice layer. Will's Copter 3x3x3 unjumbling is more related to a Helicopter cube than these others. It too is a very fun solve once unjumbled like I'm anticipating with Luke's Curvy Copter Skewb.

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Last edited by Brandon Enright on Wed Aug 29, 2012 12:48 pm, edited 1 time in total.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 12:09 pm 
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Luke wrote:
The problem with the Helicopter Skewb is that you cannot tell what the shapes of the Curvy Copter axes are (either they are rhombuses or they are trapezoids), and so it requires a lot of trial and error to unjumble the puzzle. I have solved the Curvy Copter Skewb, and I can tell you the jumbling is the easy part of it. You have the advantage of being able to see the shapes of the Curvy Copter axes, and can deal with them rather quickly.

Trial and error may be how you start out but after a while it because somewhat easy to infer the configuration of the internal edge and then it's no harder.

On TomZ's Unbandaged Helicopter Skewb, the additional unbandaging gives you enough additional freedom that you can jumble the pieces around an edge so much that sometimes inferring the internal edge configuration is hard and you really have to look at the exposed internal parts closely to figure it out.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 12:23 pm 
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Wow! Would love to see this one mass produced!
Excellent work.

-d


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 12:59 pm 
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Gorgeous!

Your Hexoid was high on my wanted list but I think this has just usurped it!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 1:21 pm 
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WOW! It looks awesome :) How big is it?


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 2:26 pm 
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Oh wow.. watching that youtube vid now.. I LOVE it. You are very right to keep this for yourself! :D Amazingly beautiful puzzle!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 2:39 pm 
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I'll take a stab at computing the number of non-jumbled positions.

First a piece survey:
  • 8 corners, 3 orientations each, no twist restriction
  • 24 curvy copter edge-wings, parity is NOT linked to the parity of the corners, no orientation
  • 24 helicopter cube triangles in 6 groups of 4
  • 24 curvy copter edge tips in 6 groups of 4
  • 24 skewb-sliced helicopter cube triangle bases in 6 groups of 4

So that should come to:
? ((8! * 24!) * (3^8) * (24! / (4! ^ 6))^3) / 24
% = 234045151851664847933712591305314853362238390730180087565516800000000000000000

Or 2.34 * 10^77 positions.

I think my strategy for solving would be reduction to Curvy Copter. They shouldn't be any parity issues with reducing to this restricted group (except a single twisted corner which you should check for and fix early in the reduction). See edits for more info on this statement.

Edit:
I previously stated there is a twist restriction on the corners. There isn't. I have updated the numbers.

Edit 2:
I incorrectly assumed the parity of the Curvy Copter edge center wings was linked to the parity of the corners. They are not. To change their parity without changing the parity of the corners, place identically colored helicopter cube triangles in the two corners that share and edge, then twist the edge 180 and undo. This will swap identically colored helicopter cube triangles and change the parity of the edge-wings.

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Last edited by Brandon Enright on Sun Apr 14, 2013 1:53 pm, edited 3 times in total.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 4:11 pm 
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Wow! .-.

That looks amazing! And i love the heart pattern :3

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Wed Aug 29, 2012 7:50 pm 
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:shock: The one 3d printed puzzle that I like enough to spend $130+ on.... wow.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Thu Aug 30, 2012 1:16 am 
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Wonderful puzzle! It has been a while since a new puzzle have been added to the family of hybrids. This is a great addition!

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Thu Aug 30, 2012 5:52 am 
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Callum wrote:
Wow! That is so crazy! Good luck solving it. I don't know if you noticed, but it actually seems a lot like Greg's Helimate in some of the ways it jumbles.

Callum


Actually the helicmate is perfectly equivalent to the heli skewb in the sense that pieces are split in half but half isn't visible. A curvy helimate would be epic, maybe I should get to it ;)

Good job Luke !

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p_dino_5.JPG [ 33.93 KiB | Viewed 7769 times ]

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Thu Aug 30, 2012 9:52 am 
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Awesome puzzle with well-edited images.
What is its edge length and its weight?

Andreas


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Thu Aug 30, 2012 12:09 pm 
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The puzzle is 57mm to an edge, and weighs approximately 100g.

Here are the other photos which I am too lazy to edit (sorry):
Attachment:
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P1050576.JPG [ 3.8 MiB | Viewed 7630 times ]

Attachment:
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P1050577.JPG [ 3.7 MiB | Viewed 7630 times ]

Attachment:
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P1050578.JPG [ 3.74 MiB | Viewed 7630 times ]

Attachment:
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P1050579.JPG [ 3.5 MiB | Viewed 7630 times ]

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3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

Buy the Curvy Copter Skewb, NovaMinx, and more here!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Aug 31, 2012 4:07 pm 
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All your puzzle designs in the last time have been exceptional.
I haven't checked out all the videos yet, but I am optimistic, that they can be turned well :P

Great and very creative concepts!
Thanks :D - Frank

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Sun Sep 02, 2012 2:12 am 
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What a fantastic design, Luke! Congratulations, I love it.

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Mon Sep 03, 2012 10:10 pm 
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Fantastic!! Amazing puzzle this one must be mass produced.


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Sep 21, 2012 11:05 am 
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Hey everyone,

Sorry for the delay, but the Curvy Copter Skewb is finally available here. There have been a number of reasons for the delay (the primary one is me being lazy), but oh well, it's available now.

It is very important when assembling this puzzle that no parts are forced into place. It is easy to assemble the puzzle without forcing the parts, however, if one is not careful you may break the feet off the Curvy Copter edge parts. I have tried to update the model with a version which has these parts thicker than on the version one, however there is apparently a problem with this new model which I have not managed to diagnose. Regardless though, if you assemble it properly there won't be any problems. I am hoping I will be able to provide some sort of assembly instruction video (if someone buys an assembled copy). Until then though, feel free to message me if you purchase a copy and I will describe to you how to assemble it.

Feel free to PM me if you have any questions! :)

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3x3x3 average of five: 8.92 seconds.
3x3x3 average of twelve: 9.77 seconds.

Buy the Curvy Copter Skewb, NovaMinx, and more here!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Sep 21, 2012 11:56 am 
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I must say this is a very gorgeous puzzle. Must be very hard to solve! I can't even imagine the solving process!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Sep 21, 2012 12:22 pm 
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I shall order one in the next few days. (I need to sort out something regarding a different Shapeways puzzle. You know about my little side project, Luke :) ) As I said earlier: A truly beautiful puzzle! :D

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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Sep 21, 2012 12:24 pm 
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I keep being baffled by its beauty, and also keep wishing I had more bucks to spare!!


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 Post subject: Re: Curvy Copter Skewb by Luke Benjii
PostPosted: Fri Sep 21, 2012 12:30 pm 
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I missed this last month. Very nice indeed!

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