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 Post subject: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 10:51 am 
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Hello TwistyPuzzles,

So, I've been looking at twistypuzzles for the past year or so and I've had a few ideas for some new puzzles.
The first idea i had was to make a cube with the eight-pointed star on the front face and have the cuts go from corner to midpoint and then to the opposite corner of the cube. I used AutoCad to come up with a rough sketch of how the puzzle would turn and the shapes of the pieces. Would anybody who is more experienced in puzzle making with an easier program such as SolidWorks try to make a working puzzle?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 11:07 am 
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Is what you mean the Dayan Gem 4?
Attachment:
gem4.jpeg
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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 11:36 am 
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Doug Roth wrote:
Is what you mean the Dayan Gem 4?

Well, that's a six-pointed star and a truncated octahedron, so I wouldn't think so.

I think I have an idea of what you mean my your description, but could you add a picture of your rough sketch just in case?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 12:58 pm 
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Not quite, the shape of the puzzle is like this (This is a really rough sketch):
The red and blue lines are independent cuts on which the puzzle turns.
The solved state is a cube but mixed up it would jumble immediately.


Attachments:
File comment: rough sketch
rough sketch.jpg
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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 2:25 pm 
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You have outlined a very interesting geometry. It's a face turning, deep-cut, whatever-this-shape-is-called:
Image

If it would turn at all then it would be a strictly jumbling puzzle.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 2:30 pm 
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I believe that is the Deltoital Icosatetrahedron.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 2:42 pm 
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The deltoidal icositetrahedron looks like this:
Attachment:
Deltoidal icositetrahedron.jpg
Deltoidal icositetrahedron.jpg [ 10.16 KiB | Viewed 5082 times ]

Its faces have only 4 edges, the shape above has pentaganol faces.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 7:21 pm 
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This is only getting more complicated, what on earth did i think up?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 7:44 pm 
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Hang on. He's talking about using a cube shape with 8-pointed star cuts. Where are you guys getting the insane shapes from? Or are those shapes related to the internal mechanism? *confused*

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Fri Nov 02, 2012 7:52 pm 
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TomZ wrote:
It's a face turning, deep-cut, whatever-this-shape-is-called:
Rock? :lol:

Maybe some kind of pentagonal icositetrahedron:



However this doesn't seem to fit the description, so CompletionNotTime, why don't you forget the cuts for now and start with the overall shape: how many faces does it have, and what shape are the faces? Then we can figure out where the cuts go.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 5:17 pm 
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Ok, considering I have never made a cube before and I'm enjoying all of your feedback, but how would i get the overall shape, i started with the cube and found a usable pattern, so how would i get the inner shape within?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 5:57 pm 
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KelvinS wrote:
However this doesn't seem to fit the description, so CompletionNotTime, why don't you forget the cuts for now and start with the overall shape: how many faces does it have, and what shape are the faces? Then we can figure out where the cuts go.

Kelvin, A Cube has 6 faces. The faces are square. Does that answer your question?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 6:13 pm 
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Tony Fisher wrote:
KelvinS wrote:
However this doesn't seem to fit the description, so CompletionNotTime, why don't you forget the cuts for now and start with the overall shape: how many faces does it have, and what shape are the faces? Then we can figure out where the cuts go.

Kelvin, A Cube has 6 faces. The faces are square. Does that answer your question?

OK, so the shape is a simple cube (not sure what TomZ was thinking), now where are the cuts?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 7:15 pm 
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Here-


Attachments:
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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 7:36 pm 
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I can understand the two cuts on the right, like a skewed 2x2x1, but what's the picture on the left and how does it relate the two on the right?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 7:49 pm 
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if you take those slices and make them at every corner, the pattern is an 8 pointed star on each face with the corners and midpoints of the faces being the points of a star. So the right is the finished puzzle. the picture on the left isolate 2 separate curs to show how the cuts are oriented on the puzzle.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sat Nov 03, 2012 7:53 pm 
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KelvinS wrote:
I can understand the two cuts on the right, like a skewed 2x2x1, but what's the picture on the left and how does it relate the two on the right?

The left is what the overall puzzle should look like, the right is just two cuts isolated to show how they would look.
I believe. This has been interesting to follow so far.
Edit, Looks like in the time I found the right wording the person who had the idea posted basically the same thing, I'll just leave this here to show how brilliant I am :lol:


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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 6:28 am 
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CompletionNotTime wrote:
if you take those slices and make them at every corner, the pattern is an 8 pointed star on each face with the corners and midpoints of the faces being the points of a star. So the right is the finished puzzle. the picture on the left isolate 2 separate curs to show how the cuts are oriented on the puzzle.

I assume you're mixing up left and right, but I think I get it now, thanks. Let me now think about the symmetry of the cuts (I can now see there are 12 cuts in total going through the center) and what shape(s) this might relate to besides a cube.

Does anyone know another puzzle that has 12 cuts going through the center? As I guess this is just a cubic form of that puzzle...

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 2:47 pm 
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Kelvin, what you are hinting at is wrong. This is not a Pentultimate or 24-Cube variation.
The shape I showed is based on the cut lines he described, if it was based on a Pentultimate I would have ended up constructing a regular dodecahedron, if it was based on a 24-Cube I would have ended up with a rhombic one.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 3:15 pm 
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Tom, as you know, the external form/geometry of any puzzle can be changed while keeping the original cuts. This includes most basic mods that we see. So all I am asking is whether there is another shape of puzzle with the same arrangement of cuts that we already know. If there isn't and the arrangement of cuts is new, then fine, but I don't think I am hinting at anything wrong here.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 3:32 pm 
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Okay, I misunderstood. I thought your questions were rhetorical.
Since they are not, I will answer them: I am 100% certain there is no such thing out there because the creation of it would be a pretty big deal. It would be a new 12-axis, deep-cut puzzle.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 3:35 pm 
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I think TomZ's solid is wrong; his solid is chiral, and this shouldn't be chiral. I think it's a deltoidical icositetrahedron, as seen earlier.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 4:42 pm 
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Coaster1235 wrote:
I think TomZ's solid is wrong; his solid is chiral, and this shouldn't be chiral. I think it's a deltoidical icositetrahedron, as seen earlier.

I agree but also disagree: I agree it should not be chiral, but it doesn't need to be deltoidal. In fact any form with 24-fold (icositetrahedral) symmetry will encompass the symmetry of the 12 cuts:


Image

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 6:54 pm 
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I think that is is the deep cut version of the deltoidal icositetrahedron. I put the coordinates of the faces (vertices of the dual rhombicuboctahedron) into a copy of Jaap's Sphere program that I downloaded (http://www.jaapsch.net/puzzles/sphere.htm), made it deep cut, and out came the following image.
Attachment:
Picture 1.png
Picture 1.png [ 42.42 KiB | Viewed 4696 times ]

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 7:26 pm 
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TomZ wrote:
I am 100% certain there is no such thing out there because the creation of it would be a pretty big deal. It would be a new 12-axis, deep-cut puzzle.
I agree.
Coaster1235 wrote:
I think TomZ's solid is wrong; his solid is chiral, and this shouldn't be chiral.
Hmmm... not as sure about this one but I too tend to think this shouldn't be chiral. However I do know how to create the solid in question. This puzzle has 12 deep cut axis. Let's step back a bit and not make it deep cut. Each cut plane then becomes 2 and each is a equal distance to the center of the puzzle and parallel to the original cut plane. So the shallow cut version has 24 cut planes and these 24 planes define the surface of the solid cut out of the center of the puzzle. If I can figure out how to express those 24 planes in POV-Ray for example it would be easy to create that shape. The thing is I suspect that is exactly what TomZ has done. So I guess the question is did he make an error doing that? Or why is the resulting shape chiral? The reflection of this puzzle in a mirror appears to be the same puzzle. However the solid (or core) presented by TomZ is NOT its own mirror image. So something very odd is happening here.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 7:34 pm 
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Question is, which of the two possible forms (pentagonal or deltoidal icositetradedron) have opposite pairs of faces which are parallel?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 7:45 pm 
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KelvinS wrote:
Question is, which of the two possible forms (pentagonal or deltoidal icositetradedron) have opposite pairs of faces which are parallel?
What makes you sure its one of these 2 forms? I suspect that its neither but I'm not sure. As for your question, I believe both have opposite faces which are parallel. I guess its time I installed POV-Ray on the new PC.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 8:04 pm 
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The deep-cut face-turning geometry of the deltoidal icositetrahedron is the one which accurately matches the idea CompletionNotTime has sketched for a cube.

If you imagine on a cube, where the perpendicular axis for one of those cutting planes ends up, the axis will exit the cube through points diagonally offset from corners of the cube (close to where the X-centers or corner-centers of a 5x5 would be). If you imagine drawing all 12 of these axes, you will have 4 lines coming out of each face, each one oriented towards an adjacent corner. If you map these to faces, this matches exactly with the geometry of the faces of a deltoidal icositetrahedron.

Because the x-centers of a 5x5 are not chiral, this geometry is also not chiral.

KelvinS wrote:
Question is, which of the two possible forms (pentagonal or deltoidal icositetradedron) have opposite pairs of faces which are parallel?


The pentagonal icositetrahedron does not have parallel opposite faces while the deltoidal one does.

EDIT: Additionally, for the other geometries KelvinS posted, the small triakis octahedron matches the geometry of the 24 wing-edges of a 5x5, and the tetrakis hexahedron matches the geometry of the 24 +centers (or edge-centers) of a 5x5.


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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 8:20 pm 
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Thanks DKwan, that has answered all my questions at once. :D

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 8:40 pm 
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Ok... POV-Ray installed and question answered. Here is your puzzle:

Attachment:
PuzzleT1.png
PuzzleT1.png [ 58.39 KiB | Viewed 4635 times ]


And here is what the core looks like:

Attachment:
PuzzleT2.png
PuzzleT2.png [ 11.96 KiB | Viewed 4635 times ]


So it is a deltoidal icositetrahedron.

And here is your POV-Ray object if anyone wants to check:

#declare puzzle = difference{
difference {
box {<-1,-1,-1>,<1,1,1> pigment {Red}}
}
union{
difference{
plane {<-1,-1,2>, +0.05}
plane {<-1,-1,2>, -0.05}
}
difference{
plane {<1,1,2>, +0.05}
plane {<1,1,2>, -0.05}
}
difference{
plane {<-1,1,2>, +0.05}
plane {<-1,1,2>, -0.05}
}
difference{
plane {<1,-1,2>, +0.05}
plane {<1,-1,2>, -0.05}
}
difference{
plane {<-1,2,-1>, +0.05}
plane {<-1,2,-1>, -0.05}
}
difference{
plane {<1,2,1>, +0.05}
plane {<1,2,1>, -0.05}
}
difference{
plane {<-1,2,1>, +0.05}
plane {<-1,2,1>, -0.05}
}
difference{
plane {<1,2,-1>, +0.05}
plane {<1,2,-1>, -0.05}
}
difference{
plane {<2,-1,-1>, +0.05}
plane {<2,-1,-1>, -0.05}
}
difference{
plane {<2,1,1>, +0.05}
plane {<2,1,1>, -0.05}
}
difference{
plane {<2,1,-1>, +0.05}
plane {<2,1,-1>, -0.05}
}
difference{
plane {<2,-1,1>, +0.05}
plane {<2,-1,1>, -0.05}
}
}
}

Carl

P.S. Arg... looks like while I was playing with POV-Ray DKwan beat me to the punch. Oh well, it was a good little POV-Ray exercise. I'm now curious how TomZ generated his image above.

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Last edited by wwwmwww on Sun Nov 04, 2012 8:59 pm, edited 1 time in total.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 8:46 pm 
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Thanks, Carl.

And congrats to Doug Roth for first identifying the symmetry - even if it was a lucky mis-identification of TomZ's mis-constructed form. :lol:

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 8:57 pm 
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DKwan wrote:
The pentagonal icositetrahedron does not have parallel opposite faces while the deltoidal one does.
Hmmm... I was about to ask if you were sure about that as I've seen pentagonal icositetrahedron dice. However it appears you are correct. Check out the info on the pentagonal icositetrahedron dice seen here:

http://www.aleakybos.ch/Shapes.htm

Carl

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 9:23 pm 
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What would this puzzle look like with the cuts on a deltoidal icositetrahedron instead of a cube?

Carl, can you do this in Povray?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 9:53 pm 
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KelvinS wrote:
Carl, can you do this in Povray?
Yes, if I had the normal of each of the planes. I'll have to think about that to see if I can figure out what they are. Note even the deep cut version would still have 24 cut planes as opposite faces are not parallel.

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 Post subject: Re: New Puzzle Cube idea
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wwwmwww wrote:
KelvinS wrote:
Carl, can you do this in Povray?
Yes, if I had the normal of each of the planes. I'll have to think about that to see if I can figure out what they are. Note even the deep cut version would still have 24 cut planes as opposite faces are not parallel.

Carl

Hang on, I thought opposite faces of the deltoidal icositetrahedron *are* parallel (unlike the pentagonal form). Also, wouldn't the 12 cutting planes be midway between and parallel to each pair of opposite faces?

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Sun Nov 04, 2012 10:41 pm 
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I think that the faces of a triakis tetrahedron could also work as the core for this puzzle the same way that the tetrahedron works for the skewb. For puzzles that are this deep cut, you only need one of each pair of antipodal axes and taking the faces of the icositetrahedron that are adjacent to every other vertex of the underlying cube gives a very symmetric way of doing that. I am not sure yet if it would have the same vertex coordinates as the catalan solid, but it should have the same arrangement of faces.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Mon Nov 05, 2012 1:37 am 
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I also get a deltoidal icositetrahedron for the underlying symmetry. Fun construction every time I did it tonight. :?

Here's what it looks like with deep face turning cuts.

Attachment:
deltoidal.jpg
deltoidal.jpg [ 63.36 KiB | Viewed 4519 times ]


Tom's right, it only scrambles by jumbling.

Does it jumble?..... Yes. Here's an example at 101.5 degrees.

Attachment:
deltoidal.2.jpg
deltoidal.2.jpg [ 75.55 KiB | Viewed 4519 times ]


And another at 180.

Attachment:
deltoidal.3.jpg
deltoidal.3.jpg [ 55.84 KiB | Viewed 4519 times ]


This thing gives me the creeps. I think making a real example would be a big accomplishment.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Mon Nov 05, 2012 2:56 am 
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Wow, that thing really is a monster, would need a few hundred parts at least.

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Mon Nov 05, 2012 9:46 am 
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KelvinS wrote:
Hang on, I thought opposite faces of the deltoidal icositetrahedron *are* parallel (unlike the pentagonal form). Also, wouldn't the 12 cutting planes be midway between and parallel to each pair of opposite faces?
Yes, sorry. I misread the question. I thought we were talking about a cube cut with deep pentagonal icositetrahedron cuts. I think io's image above answers your question.

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 Post subject: Re: New Puzzle Cube idea
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wwwmwww wrote:
I think io's image above answers your question.
Yes, it made my eyes pop out. :lol:

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Tue Nov 06, 2012 9:30 am 
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This is amazing guys, i finally know the underlying geometry of this puzzle and I really appreciate all of your enthusiasm in my idea, and it seems that we have a new prototype for somebody to make. Thanks again guys, this is awesome!

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 Post subject: Re: New Puzzle Cube idea
PostPosted: Tue Nov 06, 2012 10:45 am 
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io wrote:
I think making a real example would be a big accomplishment.
I agree.
CompletionNotTime wrote:
and it seems that we have a new prototype for somebody to make.
I believe the current record of deep cut puzzle with the most cut planes which functions well enough to be playable would be a tie between the Pentultimate and the 24-Cube both of which have 6 cut planes. This puzzle has 12 and think of the effort needed to double the 3 cut planes found in a 2x2x2 before we had the Pentultimate or 24-Cube. The Big Chop has 15 cut planes so this puzzle is certainly approaching that level of difficulty. But I see what I think is potentially and even bigger problem with this puzzle... depending on how it is made. Let's assume we had infinite precision 3D printing and could make this using the shells mechanism. A Big Chop made with the shells mechanism could have up to 2845 pieces and I think require at least 6 shells/layers. So you'd be looking at what I'd believe would be over a 1000 pieces and maybe 4 or 5 shells minimum. Since this puzzle only jumbles and the bulk of the pieces couldn't be seen from the surface I suspect it would be very easy to get in a state where it would appear the exterior pieces (the outer shell) looks like it should turn but the move would actually be blocked due to the jumbled state of the interior shells. All the shells would need to be in a turnable state to allow a particular turn and much of this info is just hidden inside the puzzle. So I think that rules out the shells mechanism as I think such a puzzle (even if it worked well) would be impossible to solve unless you had a way to see all the shells on the inside.

I haven't proven the above... just an educated guess on my part,
Carl

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