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 Post subject: Dave's Diamond
PostPosted: Mon Mar 10, 2014 2:38 pm 
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Hi Everyone,

I'm very pleased to show the results of a collaboration between Jason Smith and myself. Here is the new mechanical version of Dave's Diamond:
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If you recall, when I first showed this puzzle it was only as a magnetic prototype. After seeing Jason's puzzles made with his unique skirting rails mechanism, I thought that might be the key to making this puzzle happen. As it turns out, that was a good guess because the skirting rails concept is actually perfectly suited for the geometry of Dave's Diamond. Once Jason had the basic Solidworks model, he created the mechanism and made the print you see in these pictures.

The puzzle is a bit larger than usual in order to accommodate the mechanism. Here's a shot of it in Jason's hand:
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Here are a few more pictures showing the puzzle in various twisted states:
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As I had determined using the original magnetic prototype, the puzzle behaves like two overlapping 2x2x2 cubes. Once you start scrambling one set of 2x2x2 pieces, no other pieces can be scrambled until the puzzle is returned to its original diamond shape. After that, any other set of 2x2x2 pieces can be selected for further scrambling. Doing this a few times will result in the entire puzzle being thoroughly scrambled.

Many thanks to Jason for creating this puzzle! I'm not sure that it would have ever become a mechanical (non-magnetic) puzzle without Jason and his ingenious skirting rails.

Enjoy!
Dave


Attachments:
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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 2:43 pm 
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Wow! I want one. How does the skirting-rails structure impact putting this on Shapeways?


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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 3:02 pm 
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Great to see it stickered. Jason, did you manage to improve the turning since I tried it in at your office last week?

-Eitan

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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 3:05 pm 
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Oh yeah I really like this! The size is ok for me, I rather have a slightly bigger puzzle anyway :) Well done and it looks beautiful!


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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 3:25 pm 
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Eitan, yes, it's much better. I took it all the way apart and found a piece broken and jamming the mechanism. After reassembling I was able to do a nice scramble on it. I discovered the same thing David points out. Once you choose one of the 2x2s, you have to go back to diamond shape before being able to scramble the other. Very interesting! It still feels a bit lose though, causing jams by squishing, so before shapeways, I'd want to tweak a couple of things and reprint.

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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 4:02 pm 
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VERY nice! I know how hard this puzzle is to make, as I've attempted a shallower cut version (equivalent to 2 3x3s rather than 2x2s) which also turned out very complex.

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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 4:05 pm 
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This looks wonderful! I wonder how difficult though - will it solve like 2 2x2's? can the pieces of the two separate 2x2's intermingle?

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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 4:28 pm 
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martywolfman wrote:
can the pieces of the two separate 2x2's intermingle?

It looks like it, yes. That's what would seem to make it an interesting solving experience. Not stuck in unanalyzable jumble-land, but also not a simple matter of just finding a few commutators.


Last edited by bhearn on Tue Mar 11, 2014 1:02 pm, edited 2 times in total.

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 Post subject: Re: Dave's Diamond
PostPosted: Mon Mar 10, 2014 5:13 pm 
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Very nice puzzle ! How do we call this kind of bandaging, have we seen it before ? It reminds me a little bit of the square-1 2x2 hybrid, that you could scramble as a 2x2 or a square-1, but to make the other typ of scrambling had to be restored to a certain shape. http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3968


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 Post subject: Re: Dave's Diamond
PostPosted: Tue Mar 11, 2014 12:30 am 
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Another great mechanism story.. and a beautiful and very interesting puzzle as well. Congratulations to both Dave and Jason!

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 Post subject: Re: Dave's Diamond
PostPosted: Tue Mar 11, 2014 12:43 pm 
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bhearn wrote:
Wow! I want one.
Seconded.
bhearn wrote:
Not stuck in unanalyzable jumble-land, but also not a simple manner of just finding a few commutators.
5hinigami wrote:
How do we call this kind of bandaging, have we seen it before ? It reminds me a little bit of the square-1 2x2 hybrid, that you could scramble as a 2x2 or a square-1, but to make the other typ of scrambling had to be restored to a certain shape. http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3968
Great question! I want to say this is jumbling but this does appear to be an interesting subset of jumbling. The puzzle isn't doctrinaire but it more or less appears to be two doctrinaire puzzles linked to each other via the solved configuration of cuts (not necessarily the solved state were all colors have been restored). This puzzle and topic reminds me of this thread. Where I was trying to combine a 2x2x2, a Skewb, and a Little Chop in some interesting ways. Generally the 2x2x2 has 3 axes of rotation, the Skewb has four, and the Little Chop has 6 so one would expect a puzzle which combined all of these to have 13 axes of rotation. Though if the oriention of the base puzzles is allowed to change it can be done with as few as 10 axes. This puzzle can be thought of as two 2x2x2s that are combined after their relative orientation has been changed so this "feels" similiar to me.

May I ask what this puzzle would look like if it were modded into the shape if 2 fused cubes which had their faces parallel to the cuts in this puzzle? I can't picture it in my head easily at the moment but I suspect I might like that shape for this puzzle even more.

Great work!!! I'm eager for a video and a Shapeways offering... and pictures of the mechanism if you are willing.

Thanks,
Carl

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 Post subject: Re: Dave's Diamond
PostPosted: Tue Mar 11, 2014 3:18 pm 
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wwwmwww wrote:
May I ask what this puzzle would look like if it were modded into the shape if 2 fused cubes which had their faces parallel to the cuts in this puzzle? I can't picture it in my head easily at the moment but I suspect I might like that shape for this puzzle even more.


Yes! I made some for David while we were working on this project... Uploading here.
The images might be a bit hard to grasp. See the relation to the axis cube?


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DD_cubes.2.JPG
DD_cubes.2.JPG [ 169.76 KiB | Viewed 693 times ]
DD_cubes.1.JPG
DD_cubes.1.JPG [ 185.88 KiB | Viewed 693 times ]

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 Post subject: Re: Dave's Diamond
PostPosted: Tue Mar 11, 2014 7:45 pm 
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bhearn wrote:
martywolfman wrote:
can the pieces of the two separate 2x2's intermingle?

It looks like it, yes. That's what would seem to make it an interesting solving experience. Not stuck in unanalyzable jumble-land, but also not a simple matter of just finding a few commutators.
I'm not sure. Let me propose 2 thought experiments:

(1) Looks at the images Jason just posted showing this puzzle as the union of 2 cubes. Imagine one is white and one is black. I believe from the solved state you can choose to scrable either the white cube or the black cube. If the white cube is scrambled it never loses its cubic shape and always stays white. You can't scramble the black cube till its cubic shape is restored and then it aways stays black. I don't believe white pieces are ever intermingled with black pieces in this process. The only way I see for that to happen is if a cut on the white cube ever aligns with a cut on the black cube which allows a turn which isn't either a pure white cube 2x2x2 turn or a pure black cube 2x2x2 turn and I just don't think that ever happens. I don't have the puzzle in hand so I can't say that for sure.

(2) Now imagine both the white and black cubes being stickered with 6 colors as a normal 2x2x2 would be. Let's say the puzzle has been throughly scrambled with a mix of turns from both the black and white 2x2x2 and that in its current state only the white 2x2x2 is allowed to turn. Can the white 2x2x2 be solved with just turns of the white cube? I believe the answer is no. Here is my reasoning. I believe the cuts of the black 2x2x2 have cut up the white 2x2x2 so that it now consists of more then just the 8 corners. With just turns of the white 2x2x2 I believe only the 8 corners could be solved. The new pieces formed on the white cube by the cuts of the black 2x2x2 would require turns be made on the black 2x2x2 as well.

So while the physical pieces don't intermingle I believe the solving process has been intermingled so to speak. This puzzle I suspect is significantly more complex then just solving two seperated 2x2x2s.

Carl

P.S. One way to mix black and white pieces would be to add a new cut at the equator of the diamond. Notice the black and white cube share two opposite corners. Think of these as the poles and you can see where the equator would be. Which this leads to more questions:

(1) Would this make the puzzle easier or harder? I'm not sure.
(2) Would this equatorial cut ever align with the normal 2x2x2 cuts on either puzzle to allow some additional jumbling? I think not but again I'm not sure.

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 Post subject: Re: Dave's Diamond
PostPosted: Tue Mar 11, 2014 11:02 pm 
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I've just confirmed there are two places where slices on the "black cube" align with slices on the "white cube". They're just to either side of a 180 turn from the solved state. The hybrid slice only allows 360 degree turns, so it may as well not exist. :)

I don't think an equatorial cut would align with anything else.

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 Post subject: Re: Dave's Diamond
PostPosted: Wed Mar 12, 2014 12:37 pm 
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JasonSmith wrote:
I've just confirmed there are two places where slices on the "black cube" align with slices on the "white cube". They're just to either side of a 180 turn from the solved state. The hybrid slice only allows 360 degree turns, so it may as well not exist. :)
Very interesting. Do you have any images showing this hybrid slice? I'm very tempted to model this up in POV-Ray as two colored cubes and make a few turns and images just to see what it looks like but it will likely be a few weeks before I have time. I'm still prepping for G4G11 at the moment with what little free time I have.
JasonSmith wrote:
I don't think an equatorial cut would align with anything else.
Agreed. That equatorial cut would equate to a Skewb cut on both cubes and a hybrid 2x2x2 Skewb I don't believe allows any jumbling.

One interesting observation... if that equatorial cut were added you'd have a puzzle with 7 cuts (3 from each 2x2x2 and the extra equatorial cut). Not sure how hard that would be to do but if 7 deep cuts were possible one could apply this technique to combine two Skewbs and you'd still only need 7 deep cuts. Each Skewb needs 4 cuts but the equatorial cut would be shared between them. No idea at the moment what that would look like in your Diamond shape or how much more difficult that might be to make. And I'm also not sure how much jumbling that would allow. A very interesting area and relatively unexplored area of Twisty Puzzles feels like its being opened up by this puzzle. I'll try to model the two Skewb problem in POV-Ray as well to see if it looks interesting.

Carl

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 Post subject: Re: Dave's Diamond
PostPosted: Wed Mar 12, 2014 12:59 pm 
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I was checking my assumption about the Skewb/2x2x2 hybrid not jumbling and spotted this post by Brandon.
Brandon Enright wrote:
I wonder though: is it theoretically possible to take two non-jumbling geometries and put them together in a hybrid puzzle such that the mix does jumble?
I would say the answer is yes and this puzzle appears to be one example. The jumbling does appear very odd on this puzzle. But another example would be the hybrid of two 2x2x2s where one was simply rotated by 45 degrees about one of the turning axes. Note this puzzle would only have 5 deep cuts as one cut would be shared between the puzzles. Next question...

Is it theoretically possible to take two different non-jumbling geometries and put them together in a hybrid puzzle such that the mix does jumble?

Again I think the answer is yes but it may depend on how different. Note the second puzzle mentioned in this post could be thought of as a 2x2x2 and a 1x2x2 hybrid. Does that count as two different geometries?

I suspect a 2x2x2 and a Skewb could be joined such that they shared a common cut. The final puzzle would have a total of 6 deep cuts. I suspect that may jumble.

Carl

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 Post subject: Re: Dave's Diamond
PostPosted: Fri Mar 14, 2014 3:27 pm 
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wwwmwww wrote:
Brandon Enright wrote:
I wonder though: is it theoretically possible to take two non-jumbling geometries and put them together in a hybrid puzzle such that the mix does jumble?
I would say the answer is yes and this puzzle appears to be one example.

Well I think the answer is trivially yes: you can view the Helicopter Cube as a hybrid of three edge-turning cubes that each only has four non-overlapping turns. Or even more trivially, as a hybrid of 12 single-edge-turning cubes. Which is reduced to the point of absurdity. But is there a real question there with a more restrictive criterion?


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