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 Post subject: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 10:46 am 
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I proudly present my newest puzzle design, the Tetrahedral Twins. The puzzle could be viewed as a combination of two of Okamoto's Master Pyraminxes.
It has the shape of a stellated octahedron (stella octangula). I think it nicely illustrates some things about the symmetry of a tetrahedron.
The puzzle is 10cm on an edge so it is around the same size as a regular pyraminx.

I'm very satisfied with how it came out. The turning is nice and fluid, the mechanism is very stable: even when I unscrewed 3/4 screws it would not come apart.
The only flaw is that when halfway through one of the deep cut turns, certain pieces can wiggle a bit.

The puzzle has been printed in WSF by Shapeways and dyed black using Dylon #8. The stickers were cut by Dr. Sticker. Thanks!

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You can buy the puzzle as a DIY kit from my Shapeways shop for $260/€215. I can also offer the finished puzzle for a small extra fee. Please contact me in person for this option.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:04 am 
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Wow.
Amazing work, Tom!


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:06 am 
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That is VERY cool. I'm amazed at the design and would love to see how you actually went about designing that. I thought there wasn't enough room within the shape itself to accomodate that many pieces and such.

Very, very well done.

-DC


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:10 am 
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I've always thought there weren't enough stellated octahedrons.

Looks great!

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:19 am 
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I saw this on your shapeways a couple of weeks ago. It's nice to see that it got built :) Well done :D

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:41 am 
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fantasy creation


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 11:57 am 
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Very nice. I like the way you have sunken the sticker areas presumably to avoid them coming off when a turn goes across them.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:00 pm 
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Urgh!
Just cool.


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:15 pm 
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:shock: Amazing. Well done!

Alex

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:27 pm 
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Very cool.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:31 pm 
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NICE!!!!

Could the surfaces I've highlighted in yellow be recessed and stickered too? If so does that add anything to the puzzle? I think it does but I'm not 100% sure at the moment.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:35 pm 
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wwwmwww wrote:
If so does that add anything to the puzzle?
By stickering those pieces you reintroduce the Master Pyraminxes edges. Yes. It would add something.


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:42 pm 
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Great puzzle, and nice example of self-duality.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:53 pm 
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Andreas Nortmann wrote:
wwwmwww wrote:
If so does that add anything to the puzzle?
By stickering those pieces you reintroduce the Master Pyraminxes edges. Yes. It would add something.

You would add what is equivalent to the Skewb face-centers which are equivalent to the edges of both master pyraminxes.
I don't really fancy internal stickering though, but it could be done. If anyone seriously wants to try it out I could have the design modified in a couple of minutes.

I must mention though, the puzzle is a bit unwieldy to hold due to its shape. It works fine (I am super satisfied with how the mechanism came out) but it looks like playing with it will take some getting used to holding it.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 12:59 pm 
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Congrats Tom! This is one beautiful puzzle. Original and well built. I think it's a fair price for it.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 1:06 pm 
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Andreas Nortmann wrote:
By stickering those pieces you reintroduce the Master Pyraminxes edges. Yes. It would add something.

The reintroduction of a piece alone doesn't guaranty you've added something to the puzzle. Think of the core of this puzzle. If all this tips are taken off you basically have a Skewb Diamond.
Image
So stickering the surfaces I mentioned is the same as placing stickers on the corners of this Skewb Diamond. And I'm with you, I'm about 100% certain that adds something in this case but ask yourself what you would have if there was an easy way to reintroduce the Skewb Diamond face centers. These pieces are fixed to the pieces of the Tetrahedral Twins directly above them and as those pieces are visible, once they are solved you know the Skewb Diamond face centers have to be solved too. So reintriducing that piece doesn't add anything in this case. To prove the reintroduction of the Skewb Diamond corners adds something I think you need to prove there isn't some parity issue that forces these pieces to be solved if all the other Tetrahedral Twins pieces are solved. I don't think any such issues exist but I haven't offered a proof. The simpliest proof would probably be to offer a counter example where all the pieces of the Tetrahedral Twins have been solved yet those pieces haven't been, but without the puzzle in hand that is easier said then done.

Carl

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 1:33 pm 
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TomZ wrote:
I don't really fancy internal stickering though

In most cases I don't either. However in this case you already have pieces turning over stickered surfaces and recessed the stickered areas as a result. So the fix to sticker these internal areas would really match the rest of the puzzle. Plus, and this is the big one for me, it REALLY does give you two Master Pyraminxes in one at less then half the cost I paid for my first one.
http://twistypuzzles.com/forum/viewtopic.php?p=39153#p39153
By saying this REALLY does give you two Master Pyraminxes, I mean that all surfaces that are normally stickers on a Master Pyraminx could be solved. The one surface still hidden, the Skewb Diamond face centers (or the Skewb corners depending on how you look at it), is solved when the piece above it is solved as orientation isn't important.
TomZ wrote:
If anyone seriously wants to try it out I could have the design modified in a couple of minutes.

I'm between jobs at the moment but let me solve that problem first and I'll take you up on that offer.

Thanks,
Carl

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 1:42 pm 
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Amazing job! This looks fantastic!


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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 1:47 pm 
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Great idea for a puzzle, and it looks fantastic! Congrats, Tom.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 3:06 pm 
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Puzzle looks Great. Saw it on your shop quite a while ago, and was waiting for you to crank it out.

I like the puzzle because it disproves the common misconception that the Master Pyraminx is indeed a Master Pyraminx.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 3:07 pm 
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awesome
i want it

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 4:11 pm 
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Excellent!

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 5:26 pm 
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Tony Fisher wrote:
Very nice. I like the way you have sunken the sticker areas presumably to avoid them coming off when a turn goes across them.
Actually I had assumed that Tom followed the same logic Oskar uses when he does this for his puzzles: The nylon print does not allow stickers to adhere very well so the slight depression helps them stay on during normal handling. I think this is also a great solution for stickers that are flush against moving pieces but perhaps not the initial motivation.

Great job Tom!

Dave

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 6:18 pm 
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Great new puzzle Tom! It reminds me of a cross cube... :lol:

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 6:43 pm 
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Can you post some mech pics please? :wink: I wanted to have a look at the legs oif the extensions. :?

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 7:30 pm 
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I also saw that puzzle on your Shapeways page, but I didn't quite understand how it turned until now. I originally thought it would be quite a trivial puzzle, since I didn't expect it to turn along its central cut!

WAY COOL!

Hugo Mak wrote:
Can you post some mech pics please? :wink: I wanted to have a look at the legs oif the extensions. :?


Be careful, Hugo. I don't think anyone has ever put it in writing on the forum, but I think that asking for mech pics is considered a no-no here. It's really up to the designer to decide whether to include mech pics, and it's good to respect that. You might have more luck with a PM. (No hard feelings, Hugo! I'm sure a lot of us are eager to see the mech, but it's best to either ask in private, or figure it out yourself. 8-) )

-pi (Eitan)

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 Post subject: Re: Tetrahedral Twins
PostPosted: Tue Jan 19, 2010 7:45 pm 
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pirsquared wrote:
I also saw that puzzle on your Shapeways page, but I didn't quite understand how it turned until now. I originally thought it would be quite a trivial puzzle, since I didn't expect it to turn along its central cut!

WAY COOL!

Hugo Mak wrote:
Can you post some mech pics please? :wink: I wanted to have a look at the legs oif the extensions. :?


Be careful, Hugo. I don't think anyone has ever put it in writing on the forum, but I think that asking for mech pics is considered a no-no here. It's really up to the designer to decide whether to include mech pics, and it's good to respect that. You might have more luck with a PM. (No hard feelings, Hugo! I'm sure a lot of us are eager to see the mech, but it's best to either ask in private, or figure it out yourself. 8-) )

-pi (Eitan)

I think if you look carefully, it should be possible to get a general idea of the mechanism from the shapeways photos. :wink:
Anyways, isn't it just a master pyraminx with extensions on the centers? (It's somewhat difficult to explain)

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 5:06 am 
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DLitwin wrote:
Tony Fisher wrote:
Very nice. I like the way you have sunken the sticker areas presumably to avoid them coming off when a turn goes across them.
Actually I had assumed that Tom followed the same logic Oskar uses when he does this for his puzzles: The nylon print does not allow stickers to adhere very well so the slight depression helps them stay on during normal handling. I think this is also a great solution for stickers that are flush against moving pieces but perhaps not the initial motivation.
Actually the initial motivation was to prevent the stickers coming off during rotation, not any difficulties as far as adhesion is concerned. I've never had any problems with that but I can see how it would be a problem on puzzles with less surface area like the (mini) gigaminx. I'm planning a puzzle with smaller stickers and I think I've got a nice alternative solution that I'm going to try.

I scrambled it like a skewb and solved it. When it came to orienting the skewb corners I found an interesting cheat. I simply twisted the base into the right orientation, then permuted the pieces around it just by twisting that top and one of the skewb halves.
So it looks like showing the internal skewb corners will add something.

Since the mechanism is more or less visible on Shapeways, I'm considering adding a 3D pdf.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 9:56 am 
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TomZ wrote:
Since the mechanism is more or less visible on Shapeways, I'm considering adding a 3D pdf.

Ah. In that case can you post instructions on how to open it? I've never been able to...

Thanks!

-π (Eitan)

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 10:07 am 
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Cheese_Board wrote:
pirsquared wrote:
I also saw that puzzle on your Shapeways page, but I didn't quite understand how it turned until now. I originally thought it would be quite a trivial puzzle, since I didn't expect it to turn along its central cut!

WAY COOL!

Hugo Mak wrote:
Can you post some mech pics please? :wink: I wanted to have a look at the legs oif the extensions. :?


Be careful, Hugo. I don't think anyone has ever put it in writing on the forum, but I think that asking for mech pics is considered a no-no here. It's really up to the designer to decide whether to include mech pics, and it's good to respect that. You might have more luck with a PM. (No hard feelings, Hugo! I'm sure a lot of us are eager to see the mech, but it's best to either ask in private, or figure it out yourself. 8-) )

-pi (Eitan)

I think if you look carefully, it should be possible to get a general idea of the mechanism from the shapeways photos. :wink:
Anyways, isn't it just a master pyraminx with extensions on the centers? (It's somewhat difficult to explain)

Actually I just wanted to see how to make the extensions more stabler 'cause my design's corner legs are pretty thin.

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 10:37 am 
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wwwmwww wrote:
So stickering the surfaces I mentioned is the same as placing stickers on the corners of this Skewb Diamond. And I'm with you, I'm about 100% certain that adds something in this case but ask yourself what you would have if there was an easy way to reintroduce the Skewb Diamond face centers. These pieces are fixed to the pieces of the Tetrahedral Twins directly above them and as those pieces are visible, once they are solved you know the Skewb Diamond face centers have to be solved too. So reintriducing that piece doesn't add anything in this case. To prove the reintroduction of the Skewb Diamond corners adds something I think you need to prove there isn't some parity issue that forces these pieces to be solved if all the other Tetrahedral Twins pieces are solved. I don't think any such issues exist but I haven't offered a proof. The simpliest proof would probably be to offer a counter example where all the pieces of the Tetrahedral Twins have been solved yet those pieces haven't been, but without the puzzle in hand that is easier said then done.
You are right, that in general we need to look a bit deeper. There is an "easy" way to do that: analyze the twistability of both pieces. I am quite sure that different twistabilities mean different pieces.
But we are going away from topic.


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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 12:45 pm 
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excellent looking puzzle Tom! I guess you didn't have the same "rattling" problem with this material as I had with the FDM? Your designs are amazing! Keep it up! :)

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 1:04 pm 
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DLitwin wrote:
Tony Fisher wrote:
Very nice. I like the way you have sunken the sticker areas presumably to avoid them coming off when a turn goes across them.
Actually I had assumed that Tom followed the same logic Oskar uses when he does this for his puzzles: The nylon print does not allow stickers to adhere very well so the slight depression helps them stay on during normal handling. I think this is also a great solution for stickers that are flush against moving pieces but perhaps not the initial motivation.

Great job Tom!

Dave


I've always wondered why Oskar does that. Thanks for the info.

Great puzzle, Tom!


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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 2:44 pm 
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That looks so cool! Do you plan on selling it at all?

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 3:00 pm 
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SEBUVER wrote:
That looks so cool! Do you plan on selling it at all?
Yes, you can buy it from my Shapeways shop for just $260/€215. What a deal for TWO master pyraminxes!

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 3:33 pm 
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Ok... I was looking at this:
Image

I think it might be rather easy to take a Tetrahedral Twins puzzle and let it act like the core of a Master Dino Cube which can also turn like a Skewb. I think there are just 3 new piece types that would need to be added. One would be a tetrahedron that isn't seen on the surface. One would be half an octahedron and form the square face pieces. And the last one would be a quarter of an octahedron and form the edge pieces.

Has this Master Dino + Skewb combo been made before? Does it have a name? With these extra pieces the trivial tip rotations are no longer trivial and the "unwieldy" aspect should be gone too as we'd be back to holding a cube. If this hasn't been made yet I'm expecting to see it soon as I believe making this Tetrahedral Twins puzzle is the hard part.

I'm loving this puzzle more and more the longer I look at it. Great work.

Carl

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 Post subject: Re: Tetrahedral Twins
PostPosted: Wed Jan 20, 2010 3:58 pm 
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Has a dino+skewb actually been made to begin with?

Being a puzzle designer I wouldn't look at the puzzle you suggested that way but it seems interesting to try out. I'll get back on that soon :)

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