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 Post subject: Fractured TetrahedronPosted: Wed Feb 20, 2013 2:24 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Hello Puzzlers,

I am pleased to introduce my latest puzzle, the Fractured Tetrahedron. As you might guess, this puzzle is a fracture cut triakis tetrahedron. It has 12 sides, and four axes of rotation. Each axis is capable of 60 degree turns, but most often 120 degree turns must be used to avoid blocking adjacent axes. This is a jumbling, but not shape-shifting puzzle. It can also be thought of as a bandaged version of Timur's Skyglobe puzzle.

As with the Fractured Cube puzzle, it is not possible to assemble the Fractured Tetrahedron to achieve full symmetry. I elected to assemble it so that two vertices have one edge reversed, and two vertices have two edges reversed. This arrangement leaves two faces with a windmill pattern in the center, and two with an asymmetrical pattern in the center. I've included pictures of all vertex and face types below.

Here is the video.

You can buy Fractured Tetrahedron here.

Here are the photos:
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Fractured Tetrahedron.JPG [ 202.28 KiB | Viewed 3352 times ]
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Mid-Turn.JPG [ 203.54 KiB | Viewed 3352 times ]
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One Turn.JPG [ 193.16 KiB | Viewed 3352 times ]
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Two Turns.JPG [ 195.03 KiB | Viewed 3352 times ]
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Partial Scramble.JPG [ 189.54 KiB | Viewed 3352 times ]
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Face Type 1.JPG [ 197.38 KiB | Viewed 3352 times ]
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Face Type 2.JPG [ 193.37 KiB | Viewed 3352 times ]
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Vertex Type 1.JPG [ 192.15 KiB | Viewed 3352 times ]
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Vertex Type 2.JPG [ 205.99 KiB | Viewed 3352 times ]

Enjoy!
Dave

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 Post subject: Re: Fractured TetrahedronPosted: Wed Feb 20, 2013 6:47 pm

Joined: Sun Mar 15, 2009 12:00 am
Location: Jarrow, England
Bizarre but beautiful as always David. And very reasonably priced on Shapeways. Another one to put on my ever lengthening list of puzzles to buy

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 Post subject: Re: Fractured TetrahedronPosted: Thu Feb 21, 2013 12:08 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
I have always a love-hate for all puzzles I do not understand after 30 seconds. Puzzles like this.
David Pitcher wrote:
This is a jumbling, but not shape-shifting puzzle. It can also be thought of as a bandaged version of Timur's Skyglobe puzzle.
I am afraid this is a contradiction. I comapred it with my sample of the Skyglobe and now I second it is bandaged Skyglobe. But if it can bew viewed as a bandaged puzzle then it can't be jumbling.

The images are as perfect as ever. Thank you.
Andreas

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 Post subject: Re: Fractured TetrahedronPosted: Thu Feb 21, 2013 12:56 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Andreas Nortmann wrote:
I comapred it with my sample of the Skyglobe and now I second it is bandaged Skyglobe. But if it can bew viewed as a bandaged puzzle then it can't be jumbling.
It can still jumble due to the fact that on Skyglobe the center pentagons are fudged. This is equivalent to the relationship between Fracture-6 and Constellation Six.
Andreas Nortmann wrote:
The images are as perfect as ever. Thank you.
You are most welcome

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 Post subject: Re: Fractured TetrahedronPosted: Fri Feb 22, 2013 11:23 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
David Pitcher wrote:
It can still jumble due to the fact that on Skyglobe the center pentagons are fudged. This is equivalent to the relationship between Fracture-6 and Constellation Six.
I know that the Skyglobe is fudged. That was the reason I bought it. I should have mentioned that by myself.
Have we already discussed whether the definition of jumbling includes fudges puzzles as doctrinaire ones?

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 Post subject: Re: Fractured TetrahedronPosted: Fri Feb 22, 2013 2:20 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Andreas Nortmann wrote:
Have we already discussed whether the definition of jumbling includes fudges puzzles as doctrinaire ones?
This was discussed in the thread regarding Fracture-6. Keep in mind too that Fractured Tetrahedron is not doctrinaire. Even though it does not change shape, the slice pattern that appears on the faces does change with (almost) every turn. The only exception to this is when a vertex has all of the edge pieces pointing in the same direction (full six-way symmetry). This is true of all of the "fracture-cut" puzzles (Fractured Cube, QuadStar, Fracture-10, etc.).

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 Post subject: Re: Fractured TetrahedronPosted: Fri Feb 22, 2013 7:42 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
But if it can be viewed as a bandaged puzzle then it can't be jumbling.
Are you saying a puzzle can't both jumble and be bandaged? What do you have if you take a Helicopter Cube and glue two pieces together?

I want to say jumbling is a type of bandaging where an infinite number of pieces (but finite volume) are glued together. So I guess you could argue that if you glue two of these jumbling pieces together you just have a different jumbling puzzle. Not sure if that was where you were going with that or not.

Carl

P.S. Great looking puzzle. Though I'm still trying to understand it myself.

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 Post subject: Re: Fractured TetrahedronPosted: Sat Feb 23, 2013 3:08 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
wwwmwww wrote:
Andreas Nortmann wrote:
But if it can be viewed as a bandaged puzzle then it can't be jumbling.
Are you saying a puzzle can't both jumble and be bandaged? What do you have if you take a Helicopter Cube and glue two pieces together?
I didn't mean "bandaged" as synonym for "gluing two pieces together".
I meant "bandaged" as "something which can be reversed to make the puzzle doctrinaire".
David Pitcher wrote:
This was discussed in the thread regarding Fracture-6.
Thank you.
Sadly I can't see that we came to a result back then.
I still think the definition of jumbling has a blind spot for these cases or at least it allows misunderstandings.

BTW: Can you upload another image which shows the state when a 60°-move is possible?

Andreas

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 Post subject: Re: Fractured TetrahedronPosted: Sat Feb 23, 2013 5:53 pm

Joined: Sun Apr 30, 2006 4:17 am
Location: Düsseldorf, Germany
Hmm, seems I have to extend my list for the next Shapeways order
Your puzzles are always very aesthetic!

Great!

Frank

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 Post subject: Re: Fractured TetrahedronPosted: Sat Feb 23, 2013 6:11 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Andreas Nortmann wrote:
Can you upload another image which shows the state when a 60°-move is possible?
Sure thing (with apologies for the lighting, I didn't have time to set up my photo booth)...
Attachment:

Free Vertex.JPG [ 191.99 KiB | Viewed 2762 times ]
Andreas Nortmann wrote:
Sadly I can't see that we came to a result back then.
I still think the definition of jumbling has a blind spot for these cases or at least it allows misunderstandings.
At some point during one of the jumbling discussions I was convinced that these "fracture-cut" puzzles are indeed jumbling. But I also agree that they are slightly different from more "traditional" jumbling, and should perhaps have their own category. Then again, that may just confuse things further...

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 Post subject: Re: Fractured TetrahedronPosted: Sat Feb 23, 2013 6:39 pm

Joined: Sun May 29, 2011 2:56 pm
Location: New York
Wow, that's awesome! Your last two puzzles have been my favorite from you!

-Doug

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 Post subject: Re: Fractured TetrahedronPosted: Sun Feb 24, 2013 2:35 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
David Pitcher wrote:
]At some point during one of the jumbling discussions I was convinced that these "fracture-cut" puzzles are indeed jumbling. But I also agree that they are slightly different from more "traditional" jumbling, and should perhaps have their own category.
Therefore I will edit the description for this puzzles and will write something "it is unclear whether this is jumbling. Because of the these reasons A, B, C..."

Thank you for the image. It is still superior to most images I (or my image editing staff) have to edit.

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 Post subject: Re: Fractured TetrahedronPosted: Tue Mar 05, 2013 11:21 am

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
Andreas Nortmann wrote:
Therefore I will edit the description for this puzzles and will write something "it is unclear whether this is jumbling. Because of the these reasons A, B, C..."
The thread about Vladimir's Cheese and the discussion regarding how we define deep cut puzzles has me thinking about how we define jumbling as well. Up until now, I believe there was agreement that these "fracture cut" puzzles are jumbling. They certainly fit the definition in some ways, in that the puzzles are not doctrinaire (due to changing slice patterns with (almost) every turn), and the fact that to fully unbandage the puzzles an infinite number of cuts would be needed, reducing portions of the puzzle to dust.

However, you could argue that they differ from "traditional" jumbling in that not every turn is non-doctrinaire (not sure if I'm using that term correctly), and the puzzles never change shape. Perhaps we need to break jumbling into more than one category. For example, there is the more traditional "face-turning jumbling", as distinguished from this type of "vertex-turning jumbling". There may be more precise and descriptive ways to label the jumbling types, but the real question is whether these are two distinct phenomena. If so, I believe we should provide the clarity that two distinct terms would provide.

Any of the jumbling experts care to weigh in?

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 Post subject: Re: Fractured TetrahedronPosted: Tue Mar 05, 2013 12:14 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
TomZ pointed out that transforming ConstellationSix into Fracture-6 requires adding extra volume to the pieces not just gluing pieces together with infinitely small amounts of glue.
I don't think we need to debate this.

Therefore the important questions are:
1. Is the skyglobe (or any other fudged puzzle) a doctrinaire puzzle?
2. Is bandaging which involves adding extra volume considered as bandaging in the sense of the jumbling-definition?

If we answer both questions with "Yes" then Fractured Tetrahedron is not jumbling and we don't need to define a new type of jumbling. I am in favor of this because thinking from the behaviour Fractured Tetrahedron is a bandaged variant of something which behaves doctrinaire.

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 Post subject: Re: Fractured TetrahedronPosted: Tue Mar 05, 2013 2:02 pm

Joined: Wed Dec 10, 2008 6:26 pm
Location: Boston area
A couple thoughts come to mind:

First, can any of the face-turning jumbling geometries be fudged to the point where you have a doctrinaire puzzle, even though it may have large or small gaps (ignoring the fact that you may not be able to actually make a workable mechanism)? If so, then the only thing distinguishing such a puzzle from a fracture-cut puzzle is the shape-changing. If this is the case, then I think both types should be considered jumbling, even if further distinctions are subsequently made.

Second, any logic applied to the question at hand regarding Fractured Tetrahedron should be also applied to all of the fracture-cut puzzles. Fractured Tetrahedron happens to be the one that is closest to being a doctrinaire puzzle, but the principle of part of the puzzle being turned to dust if unbandaged still applies. It's just a matter of degree separating this example from a puzzle like Fracture-10, in which a large volume of material would be reduced to dust.

On a related but different subject, should we start a thread or other central place for such twisty puzzle specific terms? (Call it the "Twistipedia"). Many uncontroversial terms could be included (such as edge-turning, vertex-turning, face-turning, turning axis, axis system, etc.). But the more helpful stuff would be having a centralized depository of definitions for things like deep-cut, jumbling, and probably many more.

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 Post subject: Re: Fractured TetrahedronPosted: Wed Mar 06, 2013 5:18 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
This is, in fact, a jumbling puzzle. The literal shape not changing isn't all that relevant - You can also, for example, shape mod a helicopter cube to be a sphere, but it's still a jumbling puzzle. I was confused before looking up the skyglobe about the claim that this one is jumbling, because the amount of fudging necessary to fix it is so miniscule that it isn't obvious that it has to be done at all, but it's still there, so this is in fact a jumbling puzzle. If a jumbling puzzle is fudged to non-jumbling then that does change the deep character of the puzzle, making it into something rather different, so there's nothing odd about saying that a jumbling puzzle is fudged into a non-jumbling puzzle.

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 Post subject: Re: Fractured TetrahedronPosted: Wed Mar 06, 2013 6:21 pm

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
Bram wrote:
This is, in fact, a jumbling puzzle. The literal shape not changing isn't all that relevant - You can also, for example, shape mod a helicopter cube to be a sphere, but it's still a jumbling puzzle. I was confused before looking up the skyglobe about the claim that this one is jumbling, because the amount of fudging necessary to fix it is so miniscule that it isn't obvious that it has to be done at all, but it's still there, so this is in fact a jumbling puzzle. If a jumbling puzzle is fudged to non-jumbling then that does change the deep character of the puzzle, making it into something rather different, so there's nothing odd about saying that a jumbling puzzle is fudged into a non-jumbling puzzle.

Since a jumbling puzzle can be fudged into a doctrinaire/bandaged one, what would it take to make a fudged helicopter cube?

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 Post subject: Re: Fractured TetrahedronPosted: Wed Mar 06, 2013 7:48 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
rubikcollector123 wrote:
Since a jumbling puzzle can be fudged into a doctrinaire/bandaged one, what would it take to make a fudged helicopter cube?

The fudge involving the least amount of fudging, but still a huge amount, would be to make it so that the six triangles around each edge were all the exact same size and shape, and it was legal to rotate each edge multiples of 90 degrees. That would result in a doctrinaire puzzle.

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 Post subject: Re: Fractured TetrahedronPosted: Wed Mar 06, 2013 9:47 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
David Pitcher wrote:
Any of the jumbling experts care to weigh in?
I'm not really an expert but I guess I do like to play one on Twisty Puzzles.

Anyways here is my 2 cents. And as this is a post after Brams, I think its appropriate that I keep referring back to this post

Let's define a 'doctrinaire' puzzle as one where if you were to remove all the coloration then every single position would look exactly the same. The Rubik's Cube is a doctrinaire puzzle, as is the Skewb and Megaminx. Also the Sphere Xyz, Chromo Ball, Puck puzzles, and a bunch of other puzzles which don't have slices like a Rubik's Cube but still have permutations.

A shape mod is a non-doctrinaire puzzle which can be shape modded to a doctrinaire puzzle. The Fisher Cube is a shape mod, as is the Mixup Cube.

A bandage puzzle is a non-doctrinaire one where by cutting the pieces into smaller parts it's possible to transform it into a doctrinaire puzzle.

A jumble puzzle is one which is non-doctrinaire but where it isn't possible to shape mod or unbandage it into a doctrinaire puzzle.

To these definitions change:

A bandage puzzle is a non-doctrinaire one where by cutting the pieces (with zero volume or 2D surfaces) into smaller parts it's possible to transform it into a doctrinaire puzzle.

unbandage = the process of using zero volume or 2D surfaces to cut pieces into a finite number of smaller pieces.
fudging = the process of cutting up a puzzle via removing actual volume from the puzzle.

With this understand of bandaging/unbandaging and fudging then we see these definitions don't preclude that a puzzle which jumbles CAN be fudged into a doctrinaire puzzle.

I would say yes the Fractured Tetrahedron jumbles and yes it can be fudged into Timur's Skyglobe puzzle which is a doctrinaire puzzle. I think the confusion comes from the statement that the Fractured Tetrahedron "can also be thought of as a bandaged version of Timur's Skyglobe puzzle."

Maybe a better statement to make would be the Fractured Tetrahedron can also be thought of as a unfudged version of Timur's Skyglobe puzzle.

We aren't talking about a new type of Jumbling... that hasn't changed... we are talking about a different type of bandaging/unbandaging.

Conceptually I think all jumpling puzzles could be fudged into an infinite number of different doctrinaire puzzles.

Just my 2 cents,
Carl

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 Post subject: Re: Fractured TetrahedronPosted: Wed Mar 06, 2013 10:08 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
If we answer both questions with "Yes" then Fractured Tetrahedron is not jumbling and we don't need to define a new type of jumbling. I am in favor of this because thinking from the behaviour Fractured Tetrahedron is a bandaged variant of something which behaves doctrinaire.
With this argument I believe you'd be forced to conclude there are no jumbling puzzles. The difference here being that the Skyglobe was created BEFORE the Fractured Tetrahedron.

I believe ALL jumbling puzzles behave as an "un-fudged" variant of a puzzle which behaves doctrinaire. Granted most of these doctrinaire puzzles would have to be conceptual in construction at the moment as mechanisms don't exist.

Carl

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 Post subject: Re: Fractured TetrahedronPosted: Thu Mar 07, 2013 12:02 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
wwwmwww wrote:
Conceptually I think all jumbling puzzles could be fudged into an infinite number of different doctrinaire puzzles.

Yeah, it's analogous to how all irrational numbers can be approximated increasingly well be rationals.

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