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 Post subject: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 3:54 am 
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Here is a 3D Scatter Plot of all the fully-functional cuboid puzzles I know of.

[Edited 1/17:] I've added lots of reference info and links (to TP threads, websites, and YouTube videos, etc) in a new section on my website, here:
http://robspuzzlepage.com/rearrangement.htm#cuboids

I thought some of you might like it and/or find it useful...

I have omitted 1x1xn where n != 2.

Notable holes where I have found mentions of possible puzzles, but no concrete pointers to creations, are at 1x2x6, 3x4x6, 4x5x6, 5x5x7, and 10x10x10. Please point me to any solid info on those.

I also know I left out the cubic 3x5x5 made from a bandaged 6x6x6, but I included the Rylox Prism 2x4x4. I might add it later, but it opens up a can of worms regarding bandaged imitations of various other cuboids. Also, this includes only single-core designs, not multi-core/chaos/evil-twin designs.

I am aware that controversy surrounds some of the cubes larger than 7x7x7. I'm not promoting KOs - I am documenting what's out there, for the edification of collectors and enthusiasts. I won't include links to KO sources.

Attachment:
cuboids10.png
cuboids10.png [ 41.85 KiB | Viewed 1669 times ]

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Last edited by Rob on Mon Jan 18, 2010 12:09 am, edited 1 time in total.

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 4:31 am 
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That's very neat! I love it. It's a shame there is no higher resolution version though.
This would be neat in full 3D.

Just one remark: for each cuboid, there are up to 6 possible places to include it in the plot, right? What method did you use for choosing the coordinates? It looks like you used x<y<z but I'm not sure. The 1x2x2 is at (1, 2, 1) so that one does not follow the rule, but you stated that was kind of an exception.

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 4:38 am 
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That is a very clever way of categorizing(?) these puzzles. Is there a specific way you have ordered the dimensions? Have the puzzles been put where they are in increasing dimension size? So, instead of having 3x1x2, you would have 1x2x3? So really, something like the 2x2x3 could go underneath where the domino is? And the 1x2x3 underneath that? I'm sure they could, but it makes it easier to interpret it where the dimensions are in order. I think you have done this, but I am not sure.

The main problem which I see with this, (which isn't really a problem, just a downside to the type of plot) is that it is hard to see which vertical layer the puzzles are on. As I say, not a problem with this particular plot, just the general type.

Thanks for posting this though, It gives us a good idea of what cuboids have been and what (sensible) ones are still to be made.

-Mark- :)

EDIT: TomZ explained well what I am trying to get at.

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 8:41 am 
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Another try in classifying / ordering puzzles?
Well done!

Maybe (!) the z-level can be marked with thin grey lines.
I thought about a way to fill the empty space at the z=1-level of that. That would probably increase clearness. The only solution would have been to have at least one axis standing with a degree of 45° relative to the others. ...


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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 12:26 pm 
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I did this once on a sheet of paper, and wrote who made each one instead of having pictures.
Mine was in 2d, so I have 2 dimension on one side and 1 dimension on the other, but I really like the way you've done it.
It'd be nice if you made a higher resolution version, or someone could make a fully rotatably 3d version.
That'd be really cool. But, I see this being updated in the near future.

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Sun Jan 03, 2010 3:47 pm 
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Thanks for the comments!

Tom - good observation - I should have clarified to begin with.

Yes, indeed I have used k <= m <= n. So the 1x3x3 appears where it is instead of at the base of the 3x3 stack, for example.

From front to back, the first rank is 2, not 1 - I left out m=1 to save space and reduce visual clutter, and since I had no desire to include 1x1x1. It is not really needed otherwise.
The 1x2x2 and Morph are at the correct position, I believe. The "origin" in this case is 1x2x1, so I have put the 1x1x2 there since technically without the m=1 rank there is no 1x1x2 location. This is, I believe, the only puzzle that is "mis-positioned."

When I constructed this, I had all gridpoints visible in 3 dimensions, with different colors for each grid, but this results in an overly crowded and confusing display. There is no easy way to overlay the Z grid without confusion. Due to perspective, you end up with what looks like a very fine 2-D grid everywhere. That's why I did include the red "posts" - you can kind of get an idea as to the 'z' (or n) size by how high the puzzle is on its post.

If you click on the image, it brings up a slightly higher resolution image. I have scaled it to fit on an 8.5x11 sheet of paper in landscape mode. I could make a larger image but then it would be inconvenient to print.

I should also note that the puzzle images are NOT to scale.

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Mon Jan 18, 2010 12:11 am 
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Bumping...

I've added lots of reference info and links (to TP threads, websites, and YouTube videos, etc) in a new section on my website, here:
http://robspuzzlepage.com/rearrangement.htm#cuboids

(Also edited the original post.)

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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Mon Jan 18, 2010 11:43 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Urgh!
Nice effort.
Well done!


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 Post subject: Re: Cuboid 3D Scatter Plot
PostPosted: Tue Jan 19, 2010 4:56 am 
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Joined: Mon Dec 08, 2008 10:48 pm
Location: Thailand
I just seen this chart.
I would like to see mxmxn are in same row for example 3x3x2 is under 3x3x3's order.
However this chart is easy looking, where the position that we want to make new cuboid
"3x3x0" is very interesting :lol:

and I would like to see new cuboid add in this chart soon.

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