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 Post subject: Dave's Diamond V2
PostPosted: Sat Apr 26, 2014 6:39 pm 
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This is a second version of Dave's Diamond. It has been redesigned larger for stability. It's much much better, so I've also made a video showing some of the possible moves.

Video here.


For discussion of the puzzle, see the original topic here:
viewtopic.php?f=15&t=27007&hilit=dave%27s+diamond


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 Post subject: Re: Dave's Diamond V2
PostPosted: Sat Apr 26, 2014 8:09 pm 
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The conjoined universes property of this one makes it so that someone playing with it randomly will never actually scramble it - they'll start in one universe and stay there. Should make it very interesting to solve from an actually scrambled state though.

This puzzle really should be submitted to the IPP design competition. Its quite remarkable that it can be made to people familiar with prior complicated mechanisms.


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 Post subject: Re: Dave's Diamond V2
PostPosted: Sat Apr 26, 2014 8:33 pm 
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From the older thread,
bhearn wrote:
But is there a real question there with a more restrictive criterion?

How about asking if there are two non jumbling face-transitive geometries (assuming the puzzle is thought of as having the geometry of the polyhedron whose faces the puzzle's turns are based off of) which can combine to form a jumbling geometry. I may have worded that very badly but I hope you can understand what I'm getting at.

Also, will this be available on shapeways?

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 Post subject: Re: Dave's Diamond V2
PostPosted: Sat Apr 26, 2014 10:55 pm 
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Bram wrote:
This puzzle really should be submitted to the IPP design competition.
Seconded...
rayray_2561 wrote:
Also, will this be available on shapeways?
I hope so. I'm very eager to see the mechanism.

Carl

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 Post subject: Re: Dave's Diamond V2
PostPosted: Sun Apr 27, 2014 1:17 am 
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Bram wrote:
The conjoined universes property of this one makes it so that someone playing with it randomly will never actually scramble it - they'll start in one universe and stay there. Should make it very interesting to solve from an actually scrambled state though.

This puzzle really should be submitted to the IPP design competition. Its quite remarkable that it can be made to people familiar with prior complicated mechanisms.


Thanks Bram! I'm really happy that it's apparent that this one isn't easy with comventional mechanisms.

I like the term "conjoined universes", by the way.

It would be over $300 on shapeways because of the size. If there's real interest, let me know and I'll discuss with David. Perhaps a 2-cubes shapemod would be a tiny bit cheaper. David also suggested a tweak which could shrink it another 3-4 mm on an edge I think.

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 Post subject: Re: Dave's Diamond V2
PostPosted: Sun Apr 27, 2014 10:33 am 
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It's amazing to see this puzzle working so smoothly, I owe a HUGE thanks to Jason for making it happen!!!
Bram wrote:
The conjoined universes property of this one makes it so that someone playing with it randomly will never actually scramble it - they'll start in one universe and stay there. Should make it very interesting to solve from an actually scrambled state though.
This is one of the properties I found fascinating about this puzzle when I made the first magnetic prototype. And I love the term "conjoined universes".
Bram wrote:
This puzzle really should be submitted to the IPP design competition. Its quite remarkable that it can be made to people familiar with prior complicated mechanisms.
I hadn't thought of this, but we'll certainly need to give it consideration!

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 Post subject: Re: Dave's Diamond V2
PostPosted: Sun Apr 27, 2014 10:35 am 
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JasonSmith wrote:
I'm really happy that it's apparent that this one isn't easy with conventional mechanisms.
Indeed. Almost all 2x2x2's are actually 3x3x3's with the edges and face centers hidden. This is the union of two 2x2x2's but I don't think either looks much like a 3x3x3 on the inside.
JasonSmith wrote:
I like the term "conjoined universes", by the way.
Yes, I like it too. And it make me think of a question.

A 2x2x2 has 3,674,160 permutations. So here we have two 2x2x2's. Each one of those "universes" has 3,674,160 states. But how many of those states are "conjoined" to the other "universe"? If the answer was just 1 it would be the solved state and this puzzle would have 2*3,674,160 states. But I believe there are many others (where many is much less then 3,674,160). But I want to know exactly how many? What is the best way to answer this question? One way is to think of this as a shape mod of a normal 2x2x2 and to see how many different shapes it can take on. I suspect the number of permutations of each shape is the same and if so we could just divide 3,674,160 by that number to get the answer I'm after.

However Bram's conjecture "someone playing with it randomly will never actually scramble it" seems false. If the number of randomly made scrambling turns is greater then the number of shapes found above it would seem there is at least a 50% chance moves from both 2x2x2's have been sampled. Or and I missing something else?
JasonSmith wrote:
It would be over $300 on shapeways because of the size. If there's real interest, let me know and I'll discuss with David.
YES!!! YES!!! YES!!!
JasonSmith wrote:
Perhaps a 2-cubes shapemod would be a tiny bit cheaper.
Even better as that would be the shape I'd prefer. I think it would be easier to see what was going on.
JasonSmith wrote:
David also suggested a tweak which could shrink it another 3-4 mm on an edge I think.
Interesting... Just don't sacrifice turning quality to save a few extra dollars. Its a sizable investment either way so I'd prefer to have the best turning version over saving a couple dollars.

I was tempted to ask if the pieces could be cut up in such a way as to allow the two cubes to be dyed different colors. But I think that would involve cutting the polar corners into 6 pieces and most of the other pieces into two pieces so I think that is more trouble then its worth and would likely hurt the turning. A better solution would be to create this visual separation with the stickers, say 6 very light colors and 6 very dark colors.

Carl

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 Post subject: Re: Dave's Diamond V2
PostPosted: Mon Apr 28, 2014 9:51 am 
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There's definitely more than one place where you have the option of traveling between two universes. The original magnet prototype video shows one example.

One 2x2x2 has 8 corners. 2 of them will be the dipyramid points. The other 6 should have symmetrical cuts. I think this means that we'll have approximately 6! cross over points. And because you can make moves on the other 2x2x2 here, you'll actually be able to do some thorough scrambling giving you significantly more states than 2*3,674,160 states.

In an old jumbling thread I postulated the idea of a conjoined puzzles but it was for 2D sliding tiles. It is a much cooler idea to see it on a 3D twisty puzzle.

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 Post subject: Re: Dave's Diamond V2
PostPosted: Mon Apr 28, 2014 1:34 pm 
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Yes, when I played with it more yesterday, I found that I could scramble and then get back to a diamond shape pretty easily. The universes seem to have many crossover points.

From a solved state, one of the cubes can be mixed and brought back to diamond shape using R, T, T, R'

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 Post subject: Re: Dave's Diamond V2
PostPosted: Wed Apr 30, 2014 3:12 am 
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I'm not sure about the parity restrictions, but I *think* there should be six factorial connections between the two universes. The six not opposite corners can be positioned in all the spaces except the opposite one from one of the two pointy vertices, and all of their orientations will of course be set, and the orientation of the opposite vertex will be set by parity. That's 720 possibilities, which isn't a lot.


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 Post subject: Re: Dave's Diamond V2
PostPosted: Wed Apr 30, 2014 10:33 am 
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wwwmwww wrote:
I was tempted to ask if the pieces could be cut up in such a way as to allow the two cubes to be dyed different colors. But I think that would involve cutting the polar corners into 6 pieces and most of the other pieces into two pieces so I think that is more trouble then its worth and would likely hurt the turning. A better solution would be to create this visual separation with the stickers, say 6 very light colors and 6 very dark colors.
It would actually be very easy to make the two "cubes" different colors, no cutting or altering of the pieces required. You would simply make one half of the pieces one color, the other half another color, and assemble them like this:
Attachment:
dave's diamond half & half no stickers.jpg
dave's diamond half & half no stickers.jpg [ 51.34 KiB | Viewed 1342 times ]
After applying stickers, the puzzle would look something like this:
Attachment:
dave's diamond half & half color model.jpg
dave's diamond half & half color model.jpg [ 77.5 KiB | Viewed 1342 times ]
wwwmwww wrote:
Almost all 2x2x2's are actually 3x3x3's with the edges and face centers hidden. This is the union of two 2x2x2's but I don't think either looks much like a 3x3x3 on the inside.
With the skirting rails, the mechanism looks nothing at all like a 3x3x3 on the inside. In fact, it's mostly hollow space!

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 Post subject: Re: Dave's Diamond V2
PostPosted: Wed Apr 30, 2014 2:55 pm 
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This is the more literal split, but yes, I think yours is almost equivalent. It just doesn't show how the corners and faces really pair up with neighboring faces.

You could maybe do big flat black and white stickers, with colored stickers more inset than usual.


Attachments:
dave's diamond half & half no stickers2.jpg
dave's diamond half & half no stickers2.jpg [ 61.3 KiB | Viewed 1310 times ]

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 Post subject: Re: Dave's Diamond V2
PostPosted: Wed Apr 30, 2014 3:04 pm 
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If I had this puzzle in the shape of the 2 intersecting cubes, I'd use the same colour scheme on each cube, however I'd use Smaz's hollow style stickers on one cube and solid stickers on the other cube.

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 Post subject: Re: Dave's Diamond V2
PostPosted: Wed Apr 30, 2014 5:54 pm 
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JasonSmith wrote:
This is the more literal split,
Yes... this is the exact shape I was after.

Carl


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BlackWhiteCubes.png
BlackWhiteCubes.png [ 195.79 KiB | Viewed 1249 times ]

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 Post subject: Re: Dave's Diamond V2
PostPosted: Thu May 01, 2014 6:56 am 
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wwwmwww wrote:
JasonSmith wrote:
This is the more literal split,
Yes... this is the exact shape I was after.

Carl
This looks really cute :) Somehow I would prefer this shape.

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