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 Post subject: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 4:16 pm 
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Katsuhiko Okamoto added a new puzzle to his site:
http://cubepuzzle.arrow.jp/modules/pico ... p?cat_id=4

Kepler Cube

Unfortunately, as his site is still closed for non-Japanese people, I have no idea how it looks like.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 4:30 pm 
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Aww, not again! :(

I'm still dying to see the Airy Cube. Were pictures ever posted of it?

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 4:35 pm 
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Well from the name, we should have some good hint. Basically, inside a dodecahedron,
there exist EXACTLY five (equal by symmetry) inscribed cubes (i.e. each of those cubes
uses eight vertices of the dodecahedron). Those are called Kepler cubes. And as expected,
the twelve edges of each of those Kepler cubes, are simply twelve of the "face
diagonals" (not internal ones!) of the dodecahedron (i.e. the diagonals which are part
of the pentagon surfaces).

;)


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 4:41 pm 
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kastellorizo wrote:
Well from the name, we should have some good hint. Basically, inside a dodecahedron,
there exist EXACTLY five (equal by symmetry) inscribed cubes (i.e. each of those cubes
uses eight vertices of the dodecahedron). Those are called Kepler cubes. And as expected,
the twelve edges of each of those Kepler cubes, are simply twelve of the "face
diagonals" (not internal ones!) of the dodecahedron (i.e. the diagonals which are part
of the pentagon surfaces).

;)


Pantazis

Could someone please provide a visual to go along with this explanation? I would really appreciate it.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 4:47 pm 
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Strangely, I could not find a picture of it anywhere. And I was about to draw one,
when I found this video (in Chinese!):

http://www.youtube.com/watch?v=ttnj24m3 ... re=related

*********** EDIT *******************
Here's an image which illustrates the relation of the cube and the dodecahedron:

Attachment:
image058.jpg
image058.jpg [ 5.89 KiB | Viewed 6874 times ]



:)


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 5:12 pm 
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Thanks Pantazis.

If people notice, if that dodecahedron was a megaminx, the cube inside it would be a hexaminx :)

so i wonder if this is his version of a hexaminx, or some other dodecahedron > cube puzzle. speaking of, has anyone visualized a PC to cube transformation yet? :shock: i can only imagine it would be amazing! :)

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 6:07 pm 
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I believe Pantazis means this:
Image
The different colors are outlines of the cubes that combined form a dodecahedron.
I hope that because these new puzzles are not open to view to the public, they aswell will become mass produced. :)

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 6:10 pm 
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Yeap, that's a marvelous picture which is equal to a thousand words!
(ok, maybe slightly less than a thousand!)

:)


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 7:46 pm 
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that is REALLY cool!

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sat Feb 27, 2010 9:53 pm 
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Namegoeswhere wrote:
I believe Pantazis means this:
Image
The different colors are outlines of the cubes that combined form a dodecahedron.
I hope that because these new puzzles are not open to view to the public, they aswell will become mass produced. :)

All I can think of when I look at that picture is the massive starminx II

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sun Feb 28, 2010 12:45 am 
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I'm kinda lost too. what does this new puzzle look like?

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sun Feb 28, 2010 1:55 am 
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Drewseph wrote:
I'm kinda lost too. what does this new puzzle look like?



my guess is that the puzzle is some order of an NxNxN cube with a sape modification to a dodecahedron. This is only a guess

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sun Feb 28, 2010 1:12 pm 
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Thank you very much for the marvelous images. I now have a slight idea of what this could possible be.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sun Feb 28, 2010 2:09 pm 
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could it possible be a higher order hexaminx, if thats what you would even call it.
in other words:
could it be a giga/teraminx transformed into a cube?


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Sun Feb 28, 2010 2:50 pm 
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boublez wrote:
could it possible be a higher order hexaminx, if thats what you would even call it.
in other words:
could it be a giga/teraminx transformed into a cube?


I haven't known Okamoto-san to do anything tranformations of existing puzzles for quite some time now, he usually makes completely new designs, designed from scratch


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 1:21 am 
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This could be another Starminx II? Each kepler extension of the cube corresponds to a turn in Starminx II.


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 1:42 am 
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I think an edge turning dodecahedron would be a likely candidate, but that doesn't necessarily mean it will be a Starminx II.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 9:33 am 
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I thought Kepler was also the guy who proved that the planets move in elliptical orbits, so maybe his puzzle has something to do with ellipses instead?

Given Okamoto's track record to date with the super floppy cube and void cube, etc., I think he's more likely to come up with some revolutionary new mechanism like a puzzle with elliptical orbits/rotation, rather than just some other new way of slicing a dodecahedron...

Elliptical orbits would be very cool! :D

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Last edited by KelvinS on Mon Mar 01, 2010 10:07 am, edited 1 time in total.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 10:06 am 
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I'm pretty sure Kelvin is right here. That was where my mind first went, but that may be just because I am an engineer and have had lots of physics!

Mr. Okamoto generally doesn't make puzzles that other people have made before, and I'm sure he saw the pictures and video of Drew's Starminx II.

I think it's probably a puzzle so big, it makes a 3x3 revolve around it! :P

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 10:45 am 
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I'm guessing some kind of mechanism with internal cogs that make the layers of a cube rotate like the elliptical patterns produced by spirograph:
Attachment:
spirograph box.jpg
spirograph box.jpg [ 29.52 KiB | Viewed 5894 times ]

Attachment:
spirograph_12.gif
spirograph_12.gif [ 39.73 KiB | Viewed 5895 times ]

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Mon Mar 01, 2010 12:53 pm 
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TomZ wrote:
I think an edge turning dodecahedron would be a likely candidate, but that doesn't necessarily mean it will be a Starminx II.


Helicopter Dodecahedron?

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Tue Mar 02, 2010 6:41 pm 
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Kelvin Stott wrote:
Given Okamoto's track record to date with the super floppy cube and void cube, etc., I think he's more likely to come up with some revolutionary new mechanism like a puzzle with elliptical orbits/rotation, rather than just some other new way of slicing a dodecahedron...

Elliptical orbits would be very cool! :D

Agreed. I would think it would have to be some sort of new concept.


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Tue Mar 02, 2010 7:24 pm 
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Oh no!!! My efforts to divert this topic to an unrelated puzzle had failed!

Katsuhiko-san will not be happy!

*takes out his wakizashi*
*commits harakiri*


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Fri Mar 05, 2010 8:42 pm 
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It's an interesting variation. I'd say it's not a 100% new concept because others have made cube-in-cube and ball-in-cube. With cube-in-cube and ball-in-cube, when sections of the outer puzzle rotate, they could be considered to orbit around the inner one.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Wed Jun 23, 2010 8:44 pm 
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Kepler Cube
Image

Notes: Kepler Cube is a puzzle that the puzzle includes the puzzle.

History: Outside puzzle (OP) is the Void Cube. Inside puzzle (IP) is the apex turning octahedron. OP and IP are connected only by three places (marked by the stars). OP and IP synchronized rotate when the star mark is included in the rotation face. When the star mark is not included, OP and IP can respectively be rotated alone.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Wed Jun 23, 2010 9:37 pm 
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this is very odd, and very interesting. i would think it would solve somewhat like a bandaged cube. either way im sure it will be an all new challenge of its own


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Wed Jun 23, 2010 9:59 pm 
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OK this is indeed interesting. And the connection to Kepler is because of this illustration by Kepler. This illustration has all five platonic solids in it. I really doubt if anyone can make a puzzle consisting of all these shapes.


Attachments:
Kepler-751440.jpg
Kepler-751440.jpg [ 51.33 KiB | Viewed 4532 times ]
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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Wed Jun 23, 2010 11:30 pm 
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Oh wow! Awesome!

But where did you find this?


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Wed Jun 23, 2010 11:56 pm 
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Jared wrote:
Oh wow! Awesome!

But where did you find this?

http://www.puzzleworld.org/DesignCompetition/2010/


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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Thu Jun 24, 2010 1:30 am 
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That's pretty cool. I may get that at some point. It would be annoying to resticker though, with all those weird angles.

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Thu Jun 24, 2010 5:04 am 
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schuma wrote:
I really doubt if anyone can make a puzzle consisting of all these shapes.


A challenge for Oskar, maybe :lol: :lol:

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Thu Jun 24, 2010 12:13 pm 
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I can't see the picture in grigr's post. :(

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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Thu Jun 24, 2010 2:00 pm 
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kastellorizo wrote:
*takes out his wakizashi*
*commits harakiri*


Seppuku :wink:



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 Post subject: Re: new Katsuhiko Okamoto puzzle: Kepler Cube
PostPosted: Thu Jun 24, 2010 8:18 pm 
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