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 Post subject: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 10:23 am 
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I know what happens if you make all the slices regular depth - you end up with lots of itty-bitty pieces around the corners.

Why couldn't you just set up a puzzle which is an icosahedron with nine triangles on each side (like Tutt's Icosaminx) and have it turn like a face-turning octahedron, with some corner overhang? Is it doable, or would the overhang prevent turning?


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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 12:10 pm 
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I couldn't make an analog of this in UMC. And without proper visualization I can't tell you if it is possible.

Could you either please draw it up or tell me how to make it in ultimate magic cube?

(The only thing UMC can't do are spherical cuts. Which might be the answer)

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 12:38 pm 
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It cannot be done in UMC as far as I can tell.

Here's the topic for Tutt's Icosaminx: viewtopic.php?t=7369

So imagine that, but the faces turn like on a face-turning octahedron. The corners would have to have overhang, but would it still be doable somehow?


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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 12:42 pm 
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If you can't do it on UMC, you can't do it in real life unless you're doing something crazy like spherical cuts. Which might be a pretty good option.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 12:55 pm 
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The corners would definitely have some overhang. It might be doable - what you'd have to do is basically attach the corners only at the very center, and then make the rest of the pieces so that they would somehow stay in the puzzle even without the corners being there (since otherwise it would fall apart mid-turn). Imagine gelatinbrain 2.1.1, with the tiny edges removed and the center pieces cut down, so that the corners can be enlarged.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 7:08 pm 
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It would be quite easily possible in the "classic" way :)

Image

(Edit: No it's not exactly like this, but, kinda ^^)



And it's pretty nice also :)

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 7:48 pm 
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Image


take that and make it deep cut. like a halpern meir to a pyraminx. shorten edges an take out center.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 7:54 pm 
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Jared wrote:
I know what happens if you make all the slices regular depth - you end up with lots of itty-bitty pieces around the corners.

Why couldn't you just set up a puzzle which is an icosahedron with nine triangles on each side (like Tutt's Icosaminx) and have it turn like a face-turning octahedron, with some corner overhang? Is it doable, or would the overhang prevent turning?


I understand what you are saying though I believe you are seeing Tutt's Icosaminx slightly wrong. The lines do not follow the paths I believe you think you are seeing. They are slightly out. Look at every corner carefully and you should see what I mean. I am not talking about how Tutt's puzzle functions, I am talking about the face turning Icosahedron you suggest.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 9:52 pm 
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I know that the lines don't allow for such a cut, at least not a straight one. That's why I asked about overhang. (Unless I'm misunderstanding you?)


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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 10:03 pm 
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You could just make it have conical/spherical cuts like the platypus.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 10:12 pm 
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not what you wanted, but- http://twistypuzzles.com/articles/spotl ... rgen.shtml

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 10:45 pm 
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The puzzle you describe is absolutely possible :wink: though quite tricky...
The icosahedral corner pieces would have to be built very carefully to be able to spin around other pieces much like the 4x4x4 edges of Tony's Overlapping Cube.... By no means an easy feat!

In addition, it's an icosahedral based puzzle which has never been built primarily due to its low tolerance for inaccuracy and the sheer number of pieces (though after the 7x7x7, teraminx, and petaminx, this doesn't look so huge)

Gelatinbrain's 2.2.1 is indeed the exact puzzle you are looking for, except of course for the tiny pieces around the corners. These pieces are required mech-wise and make the puzzle harder, so I'm not sure why you are so interested in eliminating them.... I would keep 'em, but hey if you really want to, careful cuts and overlapping pieces have proved possible for the kilominx, Brilicube, Edges only cube and several other akwardly cutting puzzles and I see no reason why it won't work here. BUT you need to build 2.2.1 FIRST!!! :P

Peace

(Just as a small testiment to the fact that I'm not making this up and really did think about it, this puzzle would require 183 pieces (6 distinct) not counting screws, caps, etc.) 8-)


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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Thu Mar 26, 2009 11:09 pm 
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Allagem wrote:
These pieces ... make the puzzle harder

I have a pure 20 move 3-cycle (and I'm sure there are better algs), so imo the little pieces don't really make the puzzle much harder. I actually just thought of a possible solution to the whole puzzle too, so I may solve it over the weekend.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 9:48 am 
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I made this puzzle in UMC, with a slight malfunction... The corners can twist on their own, which I don't know how to remove without adding these extra pieces...


Attachments:
File comment: Remove the .txt extension.
I Faceturnig icosa.pzl.txt [601 Bytes]
Downloaded 83 times
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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 11:12 am 
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Location: Spijkenisse, the Netherlands
Tony Fisher wrote:
Jared wrote:
I know what happens if you make all the slices regular depth - you end up with lots of itty-bitty pieces around the corners.

Why couldn't you just set up a puzzle which is an icosahedron with nine triangles on each side (like Tutt's Icosaminx) and have it turn like a face-turning octahedron, with some corner overhang? Is it doable, or would the overhang prevent turning?


I understand what you are saying though I believe you are seeing Tutt's Icosaminx slightly wrong. The lines do not follow the paths I believe you think you are seeing. They are slightly out. Look at every corner carefully and you should see what I mean. I am not talking about how Tutt's puzzle functions, I am talking about the face turning Icosahedron you suggest.


Jared (probably) means the puzzle that looks like the icosaminx, but twists along the faces instead of the corners.
Mathematically seen:
Face-turning-octahedron/magic-octahedron = what-he-means/tutt´s-icosaminx

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 12:24 pm 
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Sjoerd wrote:
Tony Fisher wrote:
Jared wrote:
I know what happens if you make all the slices regular depth - you end up with lots of itty-bitty pieces around the corners.

Why couldn't you just set up a puzzle which is an icosahedron with nine triangles on each side (like Tutt's Icosaminx) and have it turn like a face-turning octahedron, with some corner overhang? Is it doable, or would the overhang prevent turning?


I understand what you are saying though I believe you are seeing Tutt's Icosaminx slightly wrong. The lines do not follow the paths I believe you think you are seeing. They are slightly out. Look at every corner carefully and you should see what I mean. I am not talking about how Tutt's puzzle functions, I am talking about the face turning Icosahedron you suggest.


Jared (probably) means the puzzle that looks like the icosaminx, but twists along the faces instead of the corners.
Mathematically seen:
Face-turning-octahedron/magic-octahedron = what-he-means/tutt´s-icosaminx


No, I think what Tony is saying is that a puzzle cannot "look" like tutt's icosaminx and turn along the faces... The cuts simply don't match up. Here is a picture to help show what he is saying.


Attachments:
Untitled.jpg
Untitled.jpg [ 23.48 KiB | Viewed 2748 times ]

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 1:30 pm 
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I know they don't match up - if the layers are of uniform depth. That's where the overhang would come in.


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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 1:39 pm 
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Ohh, I see what you're saying.. I would say that is a fairly plausible idea.

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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 2:19 pm 
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Location: Houston/San Antonio, Texas
Is this what you mean??

If so, I'd say it is very possible if you could build Gelatinbrain's 2.2.1, see my above post. :P

Peace


Attachments:
File comment: Each corner would overhang and make clearances tight
OverhangingFTI.jpg
OverhangingFTI.jpg [ 23.92 KiB | Viewed 2653 times ]
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 Post subject: Re: Theoretical face-turning icosahedron
PostPosted: Fri Mar 27, 2009 2:26 pm 
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YES that is what I meant.


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