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 Post subject: AntiRainbowPosted: Wed Aug 21, 2013 2:50 pm

Joined: Sun Mar 08, 2009 9:21 am
Location: Massachusetts, USA
The geometry of this puzzle is a strange one. At first, I tried creating a puzzle based on the geometry of the triangular orthobicupola, but doing so results in a multiple origin puzzle. I wanted a shape where the dihedral angle between two rectangles or between a rectangle and an equilateral triangle was 120°, as this allows edge pieces to be exchanged freely between these faces. The result is the shape you see here. One interesting property of this shape is that the length to width ratio of the rectangles is equal to the square root of 3, and the height of the puzzle is the same as the longer edge length of the rectangles. The puzzle measures 73mm tall, and weighs approximately 130 grams.
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VIDEO

I originally wanted to make this puzzle deeper cut than this, but I could not find a good way to do so without creating lots of tiny pieces, so I opted for these curvy cuts instead. As you can see in the pictures below, this puzzle jumbles, so I decided do a bit of unbandaging, which makes the rectangular faces appear symmetrical.

Those wondering where the name comes from: one other name for the triangular orthobicupola is the anticuboctahedron, since the shape is like a cuboctahedron that has been cut in half, rotated, and put back together. The rainbow cube is probably the best known cuboctahedron-shaped puzzle, but I also thought that this name was appropriate because the two puzzles otherwise have very little in common, but are both 14-sided.

More pictures:

Solved
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Turning
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More turning
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Jumbling
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Partially scrambled
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VIDEO

This puzzle is for sale from my Shapeways shop here for \$150 in WSF.

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 Post subject: Re: AntiRainbowPosted: Wed Aug 21, 2013 2:59 pm

Joined: Fri Dec 28, 2012 1:50 pm
Location: Near Las Vegas, NV
That looks very interesting and odd. So, essentially it is a vertex-turning trapezo-rhombic dodecahedron? Really neat!

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 Post subject: Re: AntiRainbowPosted: Wed Aug 21, 2013 4:12 pm

Joined: Fri Feb 18, 2000 8:50 am
Location: chicago, IL area U.S.A
Wow, that is really cool. Very well made! And it jumbles!

-d

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 Post subject: Re: AntiRainbowPosted: Wed Aug 21, 2013 6:17 pm

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
benpuzzles wrote:
So, essentially it is a vertex-turning trapezo-rhombic dodecahedron? Really neat!

Its not a Vertex turning trapezo rhombic dodecahedron. If it were,

1) The polyhedron would be regular

2) The other triangles would turn as well.

I still think it's an awesome puzzle! So strange.

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 Post subject: Re: AntiRainbowPosted: Wed Aug 21, 2013 6:52 pm

Joined: Sun Mar 08, 2009 9:21 am
Location: Massachusetts, USA
This is the dual shape of the AntiRainbow. It's a slightly skewed trapezo-rhombic dodecahedron. I highlighted the vertices that correspond to the turning faces on this puzzle.

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 Post subject: Re: AntiRainbowPosted: Wed Aug 21, 2013 10:22 pm

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Very cool Will! I really like the juxtaposition of simplicity and complexity. I mean simplicity in that it's shallow cut with an exposed core and not that many pieces, and, of course, complexity in the shape of the puzzle, the unbandaging, and the neat interaction between the three different face shapes.

I bet for the size (piece count), it'll offer quite a solving challenge.

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 Post subject: Re: AntiRainbowPosted: Thu Aug 22, 2013 3:59 am

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
An strangely interesting shape, and I love the curvy cuts. Is there just one type of jumbling move? Is this puzzle simulated by Gelatinbrain?

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 Post subject: Re: AntiRainbowPosted: Thu Aug 22, 2013 9:20 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Gus wrote:
Is this puzzle simulated by Gelatinbrain?

Nope.

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 Post subject: Re: AntiRainbowPosted: Thu Aug 22, 2013 11:52 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Great images for a great puzzle.
Thank you for the measurements.

Without the jumbling moves the axis system is similar to this one:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=1771
although the AntiRainbow is not deepcut for both sets of turns.

BTW:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=4326

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 Post subject: Re: AntiRainbowPosted: Thu Aug 22, 2013 1:16 pm

Joined: Mon Nov 30, 2009 1:03 pm
will_57 wrote:
This is the dual shape of the AntiRainbow. It's a slightly skewed trapezo-rhombic dodecahedron. I highlighted the vertices that correspond to the turning faces on this puzzle.
Will,

Great design! I like the partial unbandaging.

When I design jumbling puzzles, I start from the rotating vertices, like you did. The requirement is that all vertices should lie on the surface of a sphere and the distance between adjacent rotation-axis vertices should be the same. Your design satisfies this requirement. Some geometries satisfy almost but not exactly, like Jumblix. In those cases some fudging is needed. Your design looks fudge-free to me.

Oskar

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 Post subject: Re: AntiRainbowPosted: Thu Aug 22, 2013 3:00 pm

Joined: Sun Mar 08, 2009 9:21 am
Location: Massachusetts, USA
Gus wrote:
Is there just one type of jumbling move?

I think so, but I'm still not entirely sure. One thing I didn't show in the post above is that even when only making 180° turns on the rectangular faces, there are blocked moves, as in the picture below. The purple face cannot turn.
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Theoretically, one could unbandage this, but I didn't do it because it would create impossible small pieces. However, I still don't know if that would be enough to unblock all 180° (for the rectangular faces) and 120° (for the triangular faces) turns.

Also, Andreas, I'm a bit confused by the description of the puzzle in the museum. You say it's similar to a shape of a truncated tetrahedron, but I don't see the resemblance. Could you explain what you mean?

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 Post subject: Re: AntiRainbowPosted: Sat Aug 24, 2013 2:14 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
will_57 wrote:
Andreas, I'm a bit confused by the description of the puzzle in the museum. You say it's similar to a shape of a truncated tetrahedron, but I don't see the resemblance. Could you explain what you mean?
The description in the museum wrote:
truncated tetrahedron (an archimedean solid) which was further truncated on six of the edges
The second part of the sentence is important.
Another example of this truncation is demonstrated here:
http://twistypuzzles.com/articles/spotlight-jurgen/
Please refer to "Pyraminx Variations" variant b

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 Post subject: Re: AntiRainbowPosted: Sat Aug 24, 2013 3:43 am

Joined: Sun Mar 08, 2009 9:21 am
Location: Massachusetts, USA
That description isn't completely accurate, though. The shape more like a truncated tetrahedron (including the truncations along the edges) that has been cut in half, copied, and then mirrored to create the shape you see. However, this is still only an approximation, since the angles between the faces are not the same as those of the truncated tetrahedron, and the smaller triangular faces are not equilateral.

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Only on this forum would people use a V-cube 7 as a size comparison for a cat

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 Post subject: Re: AntiRainbowPosted: Sat Aug 24, 2013 8:07 am

Joined: Wed Jan 07, 2009 6:46 pm
Location: San Francisco, CA
Woah! Will this is so cool!

-Eitan

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 Post subject: Re: AntiRainbowPosted: Sat Aug 24, 2013 9:24 am

Joined: Sat Sep 15, 2012 7:42 am
Gus wrote:
An strangely interesting shape, and I love the curvy cuts. Is there just one type of jumbling move? Is this puzzle simulated by Gelatinbrain?

Less "conventional" puzzles that are not covered by Gelatinbrain are very often included in this simulator. It's not on there yet, but check back. I do not know the programmer / designer of this simulator, so I don't know who to give credit to but it's awesome!

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