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 Post subject: A new puzzle idea
PostPosted: Mon Apr 12, 2004 1:42 pm 
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I came up with a very interesting puzzle idea last night. It looks like an impossiball, and the cutting planes are the same, but there's a restriction placed on the movement - whenever one set of five triangles rotate, the opposite side must rotate in lock step with it. Alternately, you can think of it as the ends staying in place and the center band rotating. This puzzle is sort of like an equator, in that center bands move and opposite pieces always remain opposite.

There's a straightforward rubik-style mechanism for this puzzle. There are 12 pentagonal umbrellas. Unlike in the rubik's cube, the umbrella's don't rotate. The umbrellas hold down 60 little tringles, one for each umbrella edge. The little triangles hold down 30 stretched hexagons, one for each edge of the icosahedron. The stretched hexagons hold down the 20 visible pieces, which are built up to cover everything else.

I'm quite excited about this puzzle. It makes me wish I had an isolithography machine to play with :-)

There's a related puzzle which has the same relationship to the dino cube as this one has to the impossiball. That puzzle can be made in a similar way, but is quite simple to solve.


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 Post subject:
PostPosted: Mon Apr 12, 2004 7:25 pm 
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Bram,

12 pentagons? Sounds like the pentultimate? I have been spending considerable time on this lately. And I nearly had the concept cracked.


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PostPosted: Mon Apr 12, 2004 8:38 pm 
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sausage wrote:
12 pentagons? Sounds like the pentultimate? I have been spending considerable time on this lately. And I nearly had the concept cracked.


The 12 pentagons are hidden below the surface, part of the mechanism. All that's visible is the 20 big triangles. It's a technically a subgroup of the impossiball.


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PostPosted: Tue Apr 13, 2004 7:05 am 
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I can't picture how movement is physically restricted. You lose me with the description of the 30 stretched hexagons. Well, actually, I'm not even sure how all 60 triangles all stay in place!

Sandy


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 Post subject:
PostPosted: Tue Apr 13, 2004 8:48 am 
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Though the idea is clear, I don't grok the mechanism description either. I keep thinking of the Thomasball (with the fixed 12 pentagons holding the tiles in) and this may be what is confusing me.

Anyway, the slice group of the impossiball. I haven't tried it out yet, though I have played with the slice group on the megaminx and found it too difficult. That give some nice spot patterns as described by Mark Longridge on http://cubeman.org. The slice group on the impossiball might be simple enough to be fun.

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 Post subject: Re: A new puzzle idea
PostPosted: Tue Apr 13, 2004 11:29 am 
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[quote="Bram"] whenever one set of five triangles rotate, the opposite side must rotate in lock step with it. Alternately, you can think of it as the ends staying in place and the center band rotating.

i tried this with my impossiball last night and it was very interesting trying to get it back together. i did find some interesting patterns and by luck was able to get it back to a solved state.


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PostPosted: Tue Apr 13, 2004 1:18 pm 
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The slice group of the megaminx is the slice group of the imposiball plus the edges and face centers. The mechanism I suggested could be used to make that, but I agree that it's too hard, and overly tedious even when you do figure out how to solve it.

If you look at this puzzle staring directly at one triangle, then there's a distinction between the triangles on the near half and the far half. If all triangles are on the correct halves, then the solution I use for the imposiball can be done by just using the three slices which don't cause pieces to change which half they're on. My impression is that this puzzle is not overly difficult to solve.

If Jaap polishes up and posts his sphere plane intersections applet for public consumption, I'll have a much easier time explaining what my ideas and how I came up with them. I'm not nearly as good at 3d visualization as one might be led to believe. :-)


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 Post subject:
PostPosted: Tue Apr 13, 2004 6:39 pm 
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Any progress on the pentultimate? My design would have been perfect if the puzzle only had 5 cuts. But it has six... never mind.


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 Post subject:
PostPosted: Tue Apr 13, 2004 9:21 pm 
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sausage wrote:
Any progress on the pentultimate? My design would have been perfect if the puzzle only had 5 cuts. But it has six... never mind.


That sixth slice is a doozy :-) The technique I know which (in theory) works on the pentultimate and doesn't seem *too* unreasonable is one I'd like to try on the little chop first. (Little chop is the deep cut puzzle with slices running through the diagonal of two opposite faces and along two edges which connect them.)

Does anybody else have ideas for how to make a little chop? It's just as mechanically weird as pentultimate, but my suspicion is that pentultimate is too hard to be fun. Little chop is probably pretty weird too.


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 Post subject: Little Chop???
PostPosted: Tue Apr 13, 2004 11:37 pm 
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I'd like to know more about this puzzle idea. Is there anywhere I can find some drawings/design ideas?

Thanks


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 Post subject:
PostPosted: Wed Apr 14, 2004 6:06 pm 
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Bram, maybe we can get our heads together on this. I have a stack of sketched ideas I can show you. I've come to the conclusion that your original cog idea maybe the only feasable way of doing it.

I had at one stage a mechanism which I called a "necklace mechanism". Another idea occured to me last night which I need to play around with.


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 Post subject:
PostPosted: Thu Apr 15, 2004 5:06 pm 
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Guys, do you mind including me in the loop as well? I've been thinking of it a lot in the past.

Aleksey.


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 Post subject:
PostPosted: Thu Apr 15, 2004 6:46 pm 
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Came up with some more drawings on the train last night. I'm thinking the pentultimate needs to be designed with an inner layer and outer layer. Seems hopeful, I'll keep going with it and do up some 3d models.


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 Post subject:
PostPosted: Thu Apr 15, 2004 9:03 pm 
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I've been a little coy about my puzzle designs, partially because they're constantly getting tweaked and partially because I'm worried about patents and all that. Since I have way too much stuff going on in my life to be starting a business selling puzzles I should probably get over it.

I figured out a way to use ordinary gears with ordinary teeth instead of the rather obscure cogs design I had worked out. It involves attaching a gear to a 'staple' which holds together the two pieces on either side of it.

Gearing opens up a whole bunch of interesting puzzle possibilities, and the my current thought as to what's the best puzzle of the lot to try out has no visible relationship to the pentultimate whatsoever.

Puzzle mechanisms are very technical and I don't want to clutter up this list with commentary from us jarheads about them. Perhaps a wiki could be set up? That would seem to be a better medium than a forum, since we're likely to revisit the same topics over and over again.


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 Post subject:
PostPosted: Thu Apr 15, 2004 10:26 pm 
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In my view, just staples (or T on opposite ends) would be enough. No real need in gears. :P


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 Post subject:
PostPosted: Fri Apr 16, 2004 2:11 am 
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The reason behind the gears is a subtle one. In any deep cut puzzle, there's usually an inner piece which when you move the outside you have to decide which of the two halves the inner piece moves in tandem with. For the 2x2x2 this is relatively easy - there are three slices, and each piece borders all three, so you simply glue the inner ball to one of the corner pieces, and problem solved. For the pentultimate there are six slices and each of the pentagons borders on five of the six slices, so there's one internal slice which spins freely (my guess is this is the technique sausage was thinking of). The gears skirt around this in a highly general way - the internal pieces in each slice simply turn at half the rate of the pieces around them, so whenever the sides are lined up the staples are lined up.

What got me thinking about other puzzles is the idea that you could make the half speed puzzles visible. That opens up a whole lot of interesting puzzle possibilities, most of which are way too hard to be fun. I *think* I've figured out one which is scaled down enough now.


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 Post subject:
PostPosted: Fri Apr 16, 2004 6:50 am 
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We need to get together sometime and share our views and ideas. Maybe in email. That's why I asked if I could be in the loop, I've got an impression you're doing that already.

I've thought of this a lot, and yes, of course you're right about the sixth slice. In my view however you can be just fine with one pentagonal fixed to the core (fixing 5 slices of the 6), and have a specially crafter "stop stick" that is connected to the core in the sixth slice.The stop stick would no allow movement of the staples in the 6th slice, but let all other slices move freely.

Gears make the puzzle incredibly complicated in mechanism, and even more difficult to recover should one of the gears skip (which will happen one or another way!).


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 Post subject:
PostPosted: Fri Apr 16, 2004 7:32 am 
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Bram wrote:
For the pentultimate there are six slices and each of the pentagons borders on five of the six slices, so there's one internal slice which spins freely.


I'm not convinced by your reasoning. Whichever cut you choose, a piece lies on one or other side of the cut. Connecting exactly one piece to the centre of the mechanism will always theoretically keep the mechanism aligned with the pieces, provided there are no cutting planes parallel to each other.

This isn't to say this would work in practice. In your pentultimate example a pentagonal piece always has a cut parallel to it, and this is awkward. The pieces would have to hold together tightly enough and have to move smoothly enough to not cause the pentagon to twist in place when the opposite half is turned. It might be better if possible to connect one of the corner pieces to the centre.

I am ignoring completely what the actual mechanism is that actually holds the pieces together. That mechanism might impose constraints that make it impossible to connect one or both types of pieces to its centre. I'm just trying to point out that your reasoning quoted above does not apply in general.

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 Post subject:
PostPosted: Fri Apr 16, 2004 12:47 pm 
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Having an internal ball which loosely holds everything together and has a 'stop stick' to control the slice opposite the fixed pentagon *might* work. But it's tricky to keep the stop stick from having to drag through the puzzle when it's rotated about other slices. Also, this general approach tends to make a single fixed piece push a whole lot of loose pieces, and I'm afraid that the position of the single fixed piece would become excessively obvious if you were just fiddling with the puzzle.

Another possible approach is to make the inner ball have a ratcheting mechanism, so that one side of a slice could only move clockwise and the other could only move counterclockwise. This results in some very interesting engineering problems, which would likely result in a puzzle with a very distinctive feel - for example, once you started to turn a face it might get 'locked', and be impossible to turn that face back again until it's been moved to the next position first.

I just created a small mailing list for the discussion of twisty mechanisms. Anyone who would like to join it please message me.

(The prior conversations I reference once in a while were just direct communication between me and Jaap, the discussion list is new.)[/i]


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 Post subject:
PostPosted: Fri Apr 16, 2004 1:46 pm 
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Bram wrote:
Having an internal ball which loosely holds everything together and has a 'stop stick' to control the slice opposite the fixed pentagon *might* work. But it's tricky to keep the stop stick from having to drag through the puzzle when it's rotated about other slices. Also, this general approach tends to make a single fixed piece push a whole lot of loose pieces, and I'm afraid that the position of the single fixed piece would become excessively obvious if you were just fiddling with the puzzle.


I am not sure I understand the concern about the the "stop stick" having to drag through the puzzle. In my view the stick is fixed to the core, sitting permanently in one place.

Also, having a single pentagonal piece fixed to the core is very much similar to a 2x2x2 cube with one cube fixed to avoid a jam. Would that be obvious in pentultimate? I am not sure, I'd say it's not, like the 2x2x2 cube. But even so, I would not see that as a problem.

Aleksey.


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 Post subject:
PostPosted: Sun Apr 18, 2004 12:12 pm 
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hey guys. Just wanted to confirm visually... this is the dodecahedron that is much like a skewb in looks, where you turn the puzzle inhalf but instead on 4 axis this guy turns on 6?

or are you talking about something more like the pyraminx crystal?

jake


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 Post subject:
PostPosted: Sun Apr 18, 2004 6:20 pm 
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Hi Jake,

Put icosidodecahedron into google images and you can see the core shape.

Bram, I got your invite but maybe Sandy has some facility here like a private mechanism forum by invitation only? Le me know your thoughts.

The problems we face with the icosidodecahedron mech is the following:

1) A fixed pentagon to the core is an ideal solution, but still leaves one of 6 slices free, and the floating pieces holding it together can still become misaligned.

2) fixed sections. Fixed pieces holding the pieces together will not work because although a path is defined for all the slices, they will not be able to turn on the pentagon faces because of clashes.

3) teeth and gears. Possible misalignment.


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 Post subject:
PostPosted: Mon Apr 19, 2004 1:08 am 
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Bram wrote:
If Jaap polishes up and posts his sphere plane intersections applet for public consumption, I'll have a much easier time explaining what my ideas and how I came up with them.


I have polished up the applet and uploaded it.
http://www.geocities.com/jaapsch/puzzles/sphere.htm

Please use the other thread if you have any comments specifically about the applet.

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 Post subject:
PostPosted: Mon Apr 19, 2004 6:10 pm 
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Well that sucks. Jaap's page is restricted on my work proxy. Oh well.


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 Post subject: Pentultimate mechanism
PostPosted: Mon Oct 18, 2004 11:18 pm 
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Hi guys. I just joined the forum. I used to be a regular on the old cube-lovers list. I've spent the last few hours reading posts. When I came across this one, I was floored to see people discussing (and "spending considerable time" pondering!) my old Pentultimate puzzle idea. You seem to have come up with many of the same concepts (and stumbling blocks) for the mechanism that I did. Please add me to the discussion list if it is still active.

I for one would love to twist a real physical version of this puzzle. The virtual versions have proven quite a challenge, but there's nothing like that feeling of being utterly "stumped" as you fiddle and twist a real magic puzzle. Having mastered the 3x3x3 over 20 years ago, I sometimes wish for that same feeling of befuddlement!

P.S. Here's my original site for the Pentultimate:

http://www.chrisandkori.us/fw/main/defa ... DocID=1422

Chris


sausage wrote:
Bram,

12 pentagons? Sounds like the pentultimate? I have been spending considerable time on this lately. And I nearly had the concept cracked.


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