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 Post subject: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 3:42 pm 
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Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Hi Everyone,

I'm happy to introduce my latest puzzle, the OctoCube...
Attachment:
OctoCube.JPG
OctoCube.JPG [ 213.83 KiB | Viewed 2343 times ]
Attachment:
OctoCube Opposite Corner.JPG
OctoCube Opposite Corner.JPG [ 211.3 KiB | Viewed 2343 times ]

OctoCube is a shape modification of a fracture-sliced triakis octahedron, with additional corner and edge pieces added to make the shape fully cubic. The puzzle turns on six axes, much like a normal magic cube. However, when a face center displays eight-way symmetry, that axis can turn in 45 degree increments. This allows the puzzle to shape-shift as well as jumble.

You can see a video of OctoCube here.

You can also purchase OctoCube from my Shapeways shop.

Here are a few more pictures of OctoCube...
Attachment:
OctoCube Mid Twist.JPG
OctoCube Mid Twist.JPG [ 212.57 KiB | Viewed 2343 times ]
Attachment:
OctoCube Two Turns.JPG
OctoCube Two Turns.JPG [ 210.62 KiB | Viewed 2343 times ]
Attachment:
OctoCube 45 Degree Turn.JPG
OctoCube 45 Degree Turn.JPG [ 209.18 KiB | Viewed 2343 times ]
Attachment:
OctoCube Multiple Turns.JPG
OctoCube Multiple Turns.JPG [ 210.07 KiB | Viewed 2343 times ]
Attachment:
OctoCube Partial Scramble.JPG
OctoCube Partial Scramble.JPG [ 207.07 KiB | Viewed 2343 times ]

Enjoy!

Dave

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 3:44 pm 
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Joined: Mon Feb 27, 2012 10:57 am
Location: In my study drooling over my puzzle hoard - Precioussssss!
David Pitcher wrote:
Enjoy!

Oh my goodness!

When shape shifted how do you even think about solving that?

Looks amazing!

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 3:57 pm 
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Joined: Sun Mar 02, 2008 11:33 am
Location: Hiram, Ohio
Easily one of my favorites! :D


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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 4:07 pm 
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Joined: Thu Sep 17, 2009 6:07 am
Location: Germany, Bavaria
This looks absolutely incredible! :D
It is a shape mode of
Quote:
fracture-sliced triakis octahedron
Please, can you give us a hint how the original "fracture-sliced triakis octahedron" looks like? Google did not find it.

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 4:15 pm 
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Location: Bedford, England
What a fabulous looking puzzle! Wonderful work.

That does look insanely difficult to solve though.

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 4:22 pm 
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Joined: Sun Oct 04, 2009 5:06 pm
Location: Ridgefield, Connecticut
Wow, this is really, really cool. And also very affordable. I will probably end up buying one some time in the future :)


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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 4:48 pm 
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Joined: Sun May 29, 2011 2:56 pm
Location: New York
Really, really good job. One of my favorites from you, David.

-Doug

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 4:48 pm 
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Konrad wrote:
Please, can you give us a hint how the original "fracture-sliced triakis octahedron" looks like? Google did not find it.
The fracture-sliced triakis octahedron has actually never been made, but it would look like this:
Attachment:
fracture sliced triakis octahedron.jpg
fracture sliced triakis octahedron.jpg [ 71.08 KiB | Viewed 2272 times ]
I considered making this into a puzzle (Fractured Octahedron), but did not like the proportions of the pieces, with the eight sided tips being so large relative to the edge and face parts. Plus I didn't want to make another puzzle requiring 24 colors. Still, the shape kept me intrigued because it is the only one of the archimedean solids that can be made in a fully symmetrical pattern when fracture-sliced. In other words, each vertex has two opposite edge pieces flipped, and each three-sided face (of the octahedron) displays the same pattern. So I decided to shape-mod it into a cube (since it has six axes), and changed the proportions of the slice pattern to be as close to a normal 3x3x3 as possible. Voila, OctoCube!

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 5:13 pm 
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Location: The Netherlands
Wow.. absolutely gorgeous!!

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 6:11 pm 
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Location: Yaroslavl, Russia and Maryland, USA
David, I want to say that I am a huge fan of your inventions. Thank you for them. The question I ask myself each time you show us your new puzzle is when can I have it in plastic? Is there a chance that we will see them produced any time soon?

Unfortunately I dislike the material that Shapeways puzzles are made from, and so I don't consider investing into Shapeways puzzles. :oops:

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 Post subject: Re: OctoCube Puzzle
PostPosted: Thu Jan 24, 2013 6:24 pm 
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Location: San Francisco, CA
Another wonderful puzzle, David. What would it take to fully unbandage this? Could it actually be done? (i.e. Is it truly jumbling?)

-Eitan

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 Post subject: Re: OctoCube Puzzle
PostPosted: Fri Jan 25, 2013 11:39 am 
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Joined: Wed Nov 24, 2010 11:12 am
Location: Hong Kong/Beijing
A very special design. I think it must be challenging. It's not so often to see David designing a cubie shape puzzle~


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 Post subject: Re: OctoCube Puzzle
PostPosted: Fri Jan 25, 2013 2:32 pm 
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Thanks to everyone for the kind words, I really appreciate them!

Aleksey wrote:
The question I ask myself each time you show us your new puzzle is when can I have it in plastic? Is there a chance that we will see them produced any time soon?
I would love to have this happen too, but for now nothing is on the horizon. Keep asking though, and perhaps someone will hear you!

pirsquared wrote:
What would it take to fully unbandage this? Could it actually be done? (i.e. Is it truly jumbling?)
My reasoning for calling the puzzle jumbling is that the shape it was derived from (the triakis octahedron shown above) cannot be unbandaged. If additional slices were added to each face to form a five-pointed star, that star would not be regular (i.e., the center of the star is not a true pentagon). Therefore the vertex-turning triakis octahedron is a jumbling geometry.

The OctoCube is really little more than a shape-mod of the vertex-turning triakis octahedron. The edge parts of the triakis octahedron are the tiny triangles around the centers of the OctoCube, and the triangular face parts of the triakis octahedron are the small wedge-shaped edge pieces on OctoCube. I've added edge and corner pieces to make the puzzle fully cubic in shape, but that doesn't change the underlying geometry, so my conclusion is that the OctoCube jumbles too. Does that make sense?

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 Post subject: Re: OctoCube Puzzle
PostPosted: Fri Jan 25, 2013 3:45 pm 
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I'm not sure if this is what Eitan meant, but is this possible?

Attachment:
Unbandaged mixup.png
Unbandaged mixup.png [ 210.64 KiB | Viewed 1932 times ]

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 Post subject: Re: OctoCube Puzzle
PostPosted: Fri Jan 25, 2013 4:14 pm 
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JackRTully wrote:
I'm not sure if this is what Eitan meant, but is this possible?
This is also my interpretation of an unbandaged version. (Except that the 180 degree "Fisher style" moves would still not be allowed. An entirely different mechanism would be needed to accommodate the moving centers for those rotations to work.) Although it appears like the additional slices should work to unbandage the puzzle, I believe that it would not be possible because the tiny triangular pieces and the wedge-shaped edge pieces would exhibit the same jumbling properties as the edge and center parts of the vertex-turning triakis octahedron depicted above.

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 Post subject: Re: OctoCube Puzzle
PostPosted: Fri Jan 25, 2013 4:20 pm 
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Yeah I think I was going crazy with those "fisher style" moves :lol:

I apologize for not being able to find the link, but I remember reading somewhere that Oskar believes his Mixup cube is bandaged, in the sense that the outer layers can not do the 45 degree turns which is why I had wondered :)

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