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 Post subject: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 9:55 am 
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Hi Everyone,

Today I'm very pleased to introduce the TriTangle puzzle. I actually saw the possibility for this puzzle back in 2002 when I was experimenting with various prismatic shapes and looking for unique symmetries. I noticed that a diagonal slice plane through a trigonal dipyramid came very close to having 5-way symmetry. After making adjustments to the shape, I was able to create true 5-way symmetry. I made a couple of prototypes of the parts, but never got it working correctly and moved on to other projects. Recently, I took another look at the computer files, fixed the problems, and thus the TriTangle was born.

TriTangle appears to be very simple at first, since it only has seven moving parts. But the constant shape-shifting and the blocking from the large points actually makes TriTangle non-trivial to solve. Every move changes the shape of the TriTangle, and some very interesting shapes can be created. Several of them remind me of facial expressions of a fox or a fruit bat, but perhaps that's just me :wink: .

Here is the video so that you can see the TriTangle in action.

Of course you can buy TriTangle in my Shapeways shop.

And here are the pictures:
Attachment:
TriTangle Top.JPG
TriTangle Top.JPG [ 209.89 KiB | Viewed 2373 times ]
Attachment:
TriTangle Bottom.JPG
TriTangle Bottom.JPG [ 191.4 KiB | Viewed 2373 times ]
Attachment:
TriTangle One Turn.JPG
TriTangle One Turn.JPG [ 208.03 KiB | Viewed 2373 times ]
Attachment:
TriTangle Scramble 1.JPG
TriTangle Scramble 1.JPG [ 193.33 KiB | Viewed 2373 times ]
Attachment:
TriTangle Scramble 2.JPG
TriTangle Scramble 2.JPG [ 198.58 KiB | Viewed 2373 times ]
Attachment:
TriTangle Scramble 3.JPG
TriTangle Scramble 3.JPG [ 188.42 KiB | Viewed 2373 times ]
Attachment:
TriTangle Scramble 4.JPG
TriTangle Scramble 4.JPG [ 216.47 KiB | Viewed 2373 times ]
Attachment:
TriTangle Scramble 5.JPG
TriTangle Scramble 5.JPG [ 205.86 KiB | Viewed 2373 times ]
Attachment:
TriTangle Fox Face.JPG
TriTangle Fox Face.JPG [ 203.61 KiB | Viewed 2373 times ]

Enjoy!
Dave

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 10:02 am 
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Dave,

I am totally confused by the shape. What does the Jaap's Sphere of this puzzle looks like?

Oskar

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 10:13 am 
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Consider my mind boggled and my flabber well and truly ghasted. Will you stop producing these puzzles so quickly, I can't keep up!

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 10:34 am 
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Oskar wrote:
I am totally confused by the shape.
Add me to that list. I can't pull up YouTube at the moment but I'm hoping that once I see the video I'll have some idea what you've done. Would it be safe to say this is a fudged puzzle? I'm also guessing it jumbles but I actually have no clue what would happen if one tried to unbandage this puzzle. Very very interesting... I suspect if there were a metric along the lines of puzzle difficulty divided by the number of moving parts this might actually top that list in terms of twisty puzzles.

Carl

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 11:15 am 
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Oskar wrote:
I am totally confused by the shape. What does the Jaap's Sphere of this puzzle looks like?
Rather than spoiling all the fun right away, I'll wait at least a few more hours before answering this. Anyone care to take a stab at it? Andreas?

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 11:32 am 
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Location: Koblenz, Germany
Awesome.
There are three axis with turns of 72° each. Can this puzzle be explained as bandaged impossiball?
What is the angle between the three axis? Does it match the angles of a megaminx?

And my usual questions:
Edge lengths?


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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 1:23 pm 
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Location: Finland
That is truly complexity from simplicity. Very aesthetically pleasing as well :D
I'm rather sure that it would be three faces of a Kilominx with bandaged corners, which is what Andreas also proposed...
Attachment:
File comment: Three faces around a corner, with two corners bandaged on each face
quarterkilominx.png
quarterkilominx.png [ 29.52 KiB | Viewed 2261 times ]

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 4:49 pm 
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wwwmwww wrote:
Would it be safe to say this is a fudged puzzle? I'm also guessing it jumbles but I actually have no clue what would happen if one tried to unbandage this puzzle.
It is definitely not a fudged puzzle, and I'm fairly certain that it does not jumble even though it shape-shifts quite dramatically. You could potentially slice the large corners to make three pieces out of each (with no extra gaps) to unbandage the puzzle, but I'm not certain they would all retain a connection to the core.
Oskar wrote:
What does the Jaap's Sphere of this puzzle looks like?
Andreas Nortmann wrote:
There are three axis with turns of 72° each. Can this puzzle be explained as bandaged impossiball?
Andreas hit the nail on the head. I didn't realize it myself until I built the puzzle the second time in Solidworks, but it is indeed the equivalent of a section of three axes from an Impossiball. The core of the puzzle (which is the large central piece visible on the underside) is a vertex of a dodecahedron (as Coaster1235 illustrated).
Andreas Nortmann wrote:
And my usual questions:
Edge lengths?
The long edges are 4.375". the upper edges are 2.25", and the lower edges are 2.125" (all approximate).
Gus wrote:
Will you stop producing these puzzles so quickly, I can't keep up!
Ok

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 5:44 pm 
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David Pitcher wrote:
since it only has seven moving parts.
8 counting the core correct?
David Pitcher wrote:
The core of the puzzle (which is the large central piece visible on the underside) is a vertex of a dodecahedron

So I'm having a hard time matching the above with this statement:
David Pitcher wrote:
It is definitely not a fudged puzzle, and I'm fairly certain that it does not jumble even though it shape-shifts quite dramatically.
If its not fudged why does there appear to be cutouts between the core and the pieces around it as seen from the underside? If these are filled with unstickered pieces then you appear to have more then 7 moving parts. And with a bit of digging I guess that is what is going on. I found this picture.
Image
So it appears there are several small pieces inside this puzzle and I'm guessing these fill that apparent cutout region... correct?

Carl

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed Apr 25, 2012 6:06 pm 
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wwwmwww wrote:
8 counting the core correct?
Yes, the core would be the eighth part visible on the outside, and then there are the small moving pieces in between each part, but that aren't visible on the surface of the puzzle.
wwwmwww wrote:
If its not fudged why does there appear to be cutouts between the core and the pieces around it as seen from the underside?
If you are referring to the curved gaps on the underside of the puzzle, those are actually just cuts in the stickers. The large corners do meet the core directly in that area. When the large tips are rotated around they can get in to orientations where other parts rotate directly over their undersides, which would scrape the stickers off if the stickers ran all the way to the edge of the pieces. I could have created a recess for the stickers, but I liked the look of the curved cuts on them.

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 Post subject: Re: TriTangle Puzzle
PostPosted: Tue May 08, 2012 11:34 am 
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Here are a few more pictures of the TriTangle. Hopefully they help to clarify the geometry of the puzzle.

First is a shot of the TriTangle in mid-turn:
Attachment:
TriTangle Mid-Turn.JPG
TriTangle Mid-Turn.JPG [ 195.94 KiB | Viewed 1827 times ]

Next is a closeup of the mid-turn position. You can see the tips of the 5-sided core "arms" here, as well as the wedge pieces that float in between all the other pieces:
Attachment:
TriTangle Mid-Turn Closeup.JPG
TriTangle Mid-Turn Closeup.JPG [ 213.26 KiB | Viewed 1827 times ]

Last is a picture of the back of the puzzle in mid-turn. Here you can see that there is no gap between the core and the large vertex pieces of the puzzle:
Attachment:
TriTangle Mid-Turn Back.JPG
TriTangle Mid-Turn Back.JPG [ 180.25 KiB | Viewed 1827 times ]
Hopefully that clarifies some things, but please let me know if you have any more questions.

Happy puzzling!
Dave

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed May 09, 2012 9:15 am 
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hm, am I correct in saying that the three large parts are actually pyraminx crystal edges?

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed May 09, 2012 9:59 am 
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David Pitcher wrote:
Here are a few more pictures of the TriTangle.
Very nice. Thanks alot. These certainly help me understand the puzzle better.
gingervergo wrote:
hm, am I correct in saying that the three large parts are actually pyraminx crystal edges?
I'm pretty sure Coaster1235 got the picture correct above. Those large pieces are two Kilominx corners bandaged together. I find if very interesting how the need for hyperbolic cuts appears to have been avoided. Note on a Kilominx the surface of rotation doesn't all fall in the same plane at the surface of the puzzle. Here that surface of rotation appears to be a plane. The "wedge pieces that float in between all the other pieces" I believe are megaminx edges and the "tips of the 5-sided core "arms"" I believe are Megaminx face centers. If I'm right it should be possible to turn a megaminx into this puzzle through a combination of bandaging and shape modding, though I think if you were to do that you'd end up with a much bigger puzzle. What I'm less sure about is would such a puzzle be made with just extensions, or would you need to cut into the megaminx to form the "back" part of this puzzle?

Carl

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 Post subject: Re: TriTangle Puzzle
PostPosted: Wed May 09, 2012 12:46 pm 
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wwwmwww wrote:
Here that surface of rotation appears to be a plane. The "wedge pieces that float in between all the other pieces" I believe are megaminx edges and the "tips of the 5-sided core "arms"" I believe are Megaminx face centers.
The surfaces of rotation are indeed planes, and the way you've described the pieces as equivalents to the Megaminx parts is correct. It's also a better way to look at the puzzle than as a Kilominx, since it's easier to see how the slice planes are flat. To actually make a TriTangle from a Megaminx though, you would need to remove a large portion of the original puzzle, leaving only three axes in place.

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