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 Post subject: Small Stellated Dodecahedron
PostPosted: Sun Aug 27, 2006 9:25 am 
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Can anyone visualize the puzzle which the small stellated dodecahedron would form? there are some slices through it which form equilateral triangles, which could in principle be used as slicing planes, forming a puzzle with only one type of visible piece.

I don't think this would be a terribly good puzzle - it would be way too hard. But it would be fascinating to fiddle with, and a technical tour de force to construct. Unfortunately, every time I've mentioned this to people they just seem confused. So can anybody else see it, or am I just on crack?


Last edited by Bram on Sun Aug 27, 2006 10:43 am, edited 1 time in total.

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PostPosted: Sun Aug 27, 2006 10:23 am 
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I'm no expert, but I think I understand what you're asking. Since you want the puzzle to consist of all similar pieces I think that there are three choices. First, a Mobius http://www.twistypuzzles.com/cgi-bin/puzzle.cgi?pid=910 Each face would have one stelation attached. Each piece would rotate in place but not move. Second the Impossiball http://www.twistypuzzles.com/cgi-bin/puzzle.cgi?pid=576 Each face would have three 1/5 stellations attached. Third, the Dogic http://www.twistypuzzles.com/cgi-bin/puzzle.cgi?pid=643 I'm not completely sure about this one, but I think the pieces could be bandaged then build up the same way an Impossiball could be. The final pictures in the link you provided shows how an icosahedron can be built up to the small stellated dodecahedron.


Last edited by kwm on Sun Aug 27, 2006 10:54 am, edited 1 time in total.

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 Post subject:
PostPosted: Sun Aug 27, 2006 10:44 am 
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No kwm, I'm describing a very specific puzzle and asking if anybody understands what I'm talking about, not speculating about whether a puzzle with certain properties might be designable.


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 Post subject:
PostPosted: Sun Aug 27, 2006 11:10 am 
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OK, it took me going into Maya and constructing a small stellated dodecahedron (that's fun to type:)) but I see those triangular slices you're talking about.
Wow, that would be tough to make.

The red slice would be one layer in the picture. Check to see if I've got it straight


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 Post subject:
PostPosted: Sun Aug 27, 2006 11:33 am 
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Yes Tyler, that's absolutely correct.

The other nutsoid one is the disdyakis triacontahedron, which can be chopped in half, although I have some suspicions that it's surprisingly constructible, mostly because of the novel approach I came up with for the disdyakis dodecahedron.

The pentakis dodecahedron, by contrast, has quite shallow cuts and is downright tame and constructible. (Note that I'm talking about slicing it on the hexagons, not the pentagons, so pairs of adjacent faces always stay together and form a piece.)


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PostPosted: Sun Aug 27, 2006 1:13 pm 
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I see how it is sliced, and it seems to have several charactoristics of a Dogic, but not simply a build up on the puzzle or core. Althought now thinking about it, you may need to use the core. Is it a 20-leg spider, or am I still sleepy? I think it's just 12. (Just woke up).

Well, inbetween and beneath three adjacent spikes is a center on which the slice rotates. Now if you look you see there is 20 'centers' of rotation. I think your first step is to find a 20 leg spider core and work your way from there.

Now for the Pentakis Dodecahedron. That is completely possible. It's just like an odd shaped dogic. You take one of the triangles and it's 3 adjacent triangles and imagine them flat (same plane), and do that with the rest of the puzzle and you have a dogic.

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 Post subject:
PostPosted: Sun Aug 27, 2006 3:39 pm 
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Why does everybody think the only complicated puzzle is the dogic?

xcool, the dogic has a 12-armed spider at its core, same as the megaminx, corresponding, obviously, to the faces of a dodecahedron. Both the small stellated dodecahedron and the pentakis dodecahedron would require a 20-armed spider, corresponding to the faces of an icosahedron. To my knowledge, no puzzle with such a core has ever been marketed, and it would have to be built from scratch.


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 Post subject:
PostPosted: Sun Aug 27, 2006 4:29 pm 
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Pentakis Dodecahedron

Image
Image
Image

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 Post subject:
PostPosted: Sun Aug 27, 2006 4:36 pm 
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As for why people compile this with the dogic is because they assume rotating tips on your pointed parts, and also how it sticks out on a sharp angle. Do a part turn on a dogic if you don't understand. Then look at what would happen with those points if you were to turn it.

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 Post subject:
PostPosted: Sun Aug 27, 2006 5:43 pm 
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xcool, the pentagonal sections on the pentakis dodecahedron which you have marked for rotation (and which are superficially similar to the rotating tips of the dogic) are not the ones in the puzzle I mean when I say 'the pentakis dodecahedron' (although they could be added in, but that would make the puzzle more complicated and worse).

The slices which I'm talking about are the hexagons, not the pentagons, and although they're six-sided the angles aren't all exactly the same, so they can only go to three positions. The pentagonal slices are like the corners of the skewb - they look like they can rotate, but they don't. You are correct though in that if the only slices were the pentagons it would be like the dogic in that there would be non-overlapping rotating tips.


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 Post subject:
PostPosted: Sun Aug 27, 2006 7:15 pm 
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Sketch it up? MSPaint, whatever you need.

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Started cubing Oct 15 '05

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 Post subject:
PostPosted: Mon Aug 28, 2006 2:52 am 
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This puzzle doesn't look like it would be too complicated to make, it's basicaly an Anti-Alexander's Star. If I had a few Alexanders Stars to mess with I might give it a go. That is just my take, I'm sure you could make it out of a Dogic though as pointed out earlier.

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 Post subject:
PostPosted: Mon Aug 28, 2006 3:12 am 
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Scott Bedard wrote:
This puzzle doesn't look like it would be too complicated to make, it's basicaly an Anti-Alexander's Star. If I had a few Alexanders Stars to mess with I might give it a go. That is just my take, I'm sure you could make it out of a Dogic though as pointed out earlier.


I don't think it is as simple as calling it a anti Alexanders Star (thought so first, but changed opinion as I read through the tread).

From what I can see in the picture every single triangular face of this puzzle (20*5=100) would be their own movable piece.
And evey twist would affect nine spikes instead of the six on the Alexanders Star. (three spikes compleatly change place in a 3-cycle (depending on how it would actually solve it might also permute all faces of the spikes, right?), the other six get two of their five faces circled round in groups of three)


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 Post subject:
PostPosted: Mon Aug 28, 2006 7:42 am 
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Scott, the small stellated dodecahedron couldn't possibly be made out of a dogic or an alexander's star. For starters, the small stellated dodecahedron has three positions for each slice, while those others have five.


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 Post subject:
PostPosted: Mon Aug 28, 2006 7:53 am 
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Yes Haara, when you slice it three of the spikes moves as complete units and three others have two pieces shaved off each.


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 Post subject:
PostPosted: Mon Aug 28, 2006 7:57 am 
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Bram wrote:
Yes Haara, when you slice it three of the spikes moves as complete units and three others have two pieces shaved off each.


That was kind of what I said, I just had a bad look at the picture and said that there were six spikes not moving entirely...

I hereby stand corrected *it is free to judge wether it is by me or Bram :P*


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