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 Post subject: Fractured Cube
PostPosted: Fri Nov 02, 2012 2:05 pm 
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Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Hello Everyone,

I'm happy to introduce my latest puzzle, the Fractured Cube:
Attachment:
Vertex Type 1.JPG
Vertex Type 1.JPG [ 201.54 KiB | Viewed 2468 times ]
Fractured Cube is based on the geometry of the tetrakis hexahedron. It has 24 sides, and it is a jumbling, but not shape-shifting puzzle. It turns on eight axes, once located at each vertex showing six-way symmetry. Each axis can turn in increments of 60 degrees. But most often 60 degree turns will block adjacent axes, so 120 degree turns need to be used unless the axis being turned has all of the edges pointing in the proper direction.

The parts for the puzzle actually could have been arranged in a couple of different ways, but they could not have been arranged to create complete symmetry. I chose to orient the edges such that at the start there are four axes with one edge flipped, and four axes with two edges flipped. This creates four "faces" with a windmill pattern, and the other two faces show a symmetrical (butterfly?) pattern.

Here is the video of Fractured Cube.

You can buy Fractured Cube in my Shapeways shop.

Here are a few more pictures of the puzzle:
Attachment:
Vertex Type 2.JPG
Vertex Type 2.JPG [ 198.63 KiB | Viewed 2468 times ]
Attachment:
Windmill Face.JPG
Windmill Face.JPG [ 214.52 KiB | Viewed 2468 times ]
Attachment:
Symmetric Face.JPG
Symmetric Face.JPG [ 197.39 KiB | Viewed 2468 times ]
Attachment:
One Turn.JPG
One Turn.JPG [ 200.38 KiB | Viewed 2468 times ]
Attachment:
Mid Turn.JPG
Mid Turn.JPG [ 203.87 KiB | Viewed 2468 times ]
Attachment:
60 Degree Turn.JPG
60 Degree Turn.JPG [ 203.12 KiB | Viewed 2468 times ]
Attachment:
Multiple Turns.JPG
Multiple Turns.JPG [ 213.67 KiB | Viewed 2468 times ]

Enjoy!
Dave

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Visit Pitcher Puzzles where you can buy the IPP award-winning RotoPrism 2, Fracture-10, and many, many more.


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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 2:52 pm 
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Joined: Mon Jun 14, 2010 6:59 pm
Location: Crestwood, IL
I really like this one! It looks like it would be very confusing to solve and boggles the mind just looking at it. So beautiful! :)


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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 2:56 pm 
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Joined: Sun May 29, 2011 2:56 pm
Location: New York
I also really like this. This would be a beast to solve.

-Doug

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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 4:02 pm 
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Location: Marin, CA
David, all your puzzles are great and this is no exception. You keep making me want to switch to black puzzles.
It wasn't obvious to me that a symmetrical version couldn't be made, but I see why now after mentally walking around the shape a little.

I really like this.

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Jason Smith posted here as 'io' through 2012.
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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 4:48 pm 
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Location: Bay Area, California
Beautiful! I'm not sure I quite follow the geometry of this just yes so I'll have to think about it some more.

It reminds me of Eric Vergo's Compound Crystal which is another beauty.

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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 6:10 pm 
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io wrote:
David, all your puzzles are great and this is no exception.
I totally agree. This looks great!

Carl

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 Post subject: Re: Fractured Cube
PostPosted: Fri Nov 02, 2012 9:00 pm 
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Can you explain why it jumbles? It looks unbandageable to me but I'm probably missing something.


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 Post subject: Re: Fractured Cube
PostPosted: Sat Nov 03, 2012 8:55 pm 
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Awesome! Why?! Why!? Why?! Why your puzzle gets mass produced? :D

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 Post subject: Re: Fractured Cube
PostPosted: Sat Nov 03, 2012 9:15 pm 
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Location: Australia
This is a real showstopper isn't it? Masterpiece.

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 Post subject: Re: Fractured Cube
PostPosted: Sun Nov 04, 2012 10:49 am 
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Thanks for all the kind words, they are always so nice to read!

Jared wrote:
Can you explain why it jumbles? It looks unbandageable to me but I'm probably missing something.
Sure thing. The proof is similar to the jumbling proof for the QuadStar puzzle. Here is an image of one face of the Fractured Cube, with a few additional cuts:
Attachment:
jumbling proof.JPG
jumbling proof.JPG [ 60.97 KiB | Viewed 2056 times ]
As you can see, the new cuts do not line up to create equal size and shaped pieces. In order for the puzzle to be unbandaged, the cut lines shown would need to form a five-pointed star, but the proportions of the triangular faces do not allow this.
io wrote:
It wasn't obvious to me that a symmetrical version couldn't be made, but I see why now after mentally walking around the shape a little.
Interestingly, you could arrange the pieces so that every "face" has the same pattern (in this case the "butterfly" pattern). Four corners would have three edges reversed, and four would have no edges reversed. Even though it might seem like a more appealing starting pattern (being somewhat more symmetrical), this would prohibit the three correctly oriented edges at the four axes with three edges reversed from ever becoming scrambled, since those four axes would be permanently limited to 120 degree moves.

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Visit Pitcher Puzzles where you can buy the IPP award-winning RotoPrism 2, Fracture-10, and many, many more.


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