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 Post subject: Tridiminished icosahedron puzzle idea
PostPosted: Mon Jun 20, 2011 1:24 pm 
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Hello everyone.

Few days ago interesting puzzle idea came to my mind. I was reading about Johnson's Solids on Wikipedia when I found tridiminished icosahedron. I haven't found here any puzzle based on this shape so I tried design it myself. However I'm not sure how should it be done correctly. Here's my attempt.

Image

In above render each color represents different kind of piece. This puzzle has 4 planes of rotation (4 cuts):

Face-turning cut...
Image

...and 3 edge-turning cuts.

Image

There's also possible jumbling-move on about 63 degrees (I haven't yet checked if it allows another moves on this mechanism, but I guess yes). The reason cut deepness is made way you see is I found it rather optimal both in appearance and mechanism. (of course I may be wrong :))
Image

And mechanism now. Edge-turning moves are allowed by using spherical 'rails' (hope you know what I mean ;p).
Image

As you can see bottom piece of the puzzle is its core. That cylindrical thing is the analog of standard 3x3 cube 3-d cross (place where screws are placed).
Puzzle has also 4 more screws, however they're not stationary but floating.
Image

This should allow horizontal layer to move correctly.
Image

Screws and circular 'rails' should keep upper blue and orange pieces in place.
Ok. This was my concept of mechanism, but there is one (at least) problem. On third and fourth pictures (edge-turn & jumble-turn) you can see that orange corners could easily fall off. Same thing happens if we turn edge-layer by 90 degree.
Image

Three upper pieces aren't kept in place by anything. (similar pieces on left and right can be moved but won't fall off because of puzzle shape).
I found few solutions to this. First is to pillowing the puzzle. Second idea is to not making horizontal cut, but I'm afraid that puzzle would be to easy to solve due to only 3 cuts. Horizontal cut can be made also from the bottom, but it would make mechanism more complicated. I'm not pleased with those three, so I need your advice :)
What can be done here to improve the design?
Also, feel free to design your own version if you wish (I believe you can make it way better since I don't have much experience).

Krystian


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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Mon Jun 20, 2011 3:52 pm 
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I definitely like the idea. As for the mechanism, I didn't take a close enough look but does that bottom core piece eliminate some functionality? If so, then it would be better if you could find a way to restore functionality.

As for the issue of the unsecured pieces, I think that pillowing is the best way to go (strictly from an "outsider's" perspective)

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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Mon Jun 20, 2011 6:22 pm 
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madartilect wrote:
I found few solutions to this. First is to pillowing the puzzle. Second idea is to not making horizontal cut, but I'm afraid that puzzle would be to easy to solve due to only 3 cuts.

The horizontal cut never jumbles or is allowed to turn while the puzzle is jumbled... I believe. So you can only use this cut without jumbling moves. Then note this cut makes your orange, purple, and blue pieces. Without jumpling moves these pieces can either be on the top turnable side or on one of 3 other storage sides where they aren't allowed to turn. As such I think it should be fairly easy to solve just these pieces and I'm not sure they add much to the puzzle. That said I think you may be under selling the complexity of the puzzle with the 3 cuts. Its hard to say for sure but its those cuts that I think make the most interesting pieces. I'd say make your puzzle with the 3 cuts first and come back and revisit this one later. Pillowing is the only thing I'm sure would solve the issue but I'd personally prefer a non-pillowed 3 cut version more.

Carl

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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Tue Jun 21, 2011 8:19 am 
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This is a very interesting shape to use as the foundation for a puzzle, but I think the slice pattern would look better if the cuts are moved deeper, and the horizontal cut moved to the bottom half of the puzzle. Here's an image of the reworked design:
Attachment:
icosahedron tridiminished.jpg
icosahedron tridiminished.jpg [ 56.24 KiB | Viewed 2071 times ]
If it's possible to use this pattern without having pieces fall out mid-turn, I think it would retain the more challenging aspects of the concept while enhancing the aesthetics.

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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Tue Jun 21, 2011 12:53 pm 
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quicksolver wrote:
As for the issue of the unsecured pieces, I think that pillowing is the best way to go (strictly from an "outsider's" perspective)

Or nonplanar cuts. AKA Make that puzzle curvy as heck! We like curvy lines!

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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Thu Jun 23, 2011 8:10 am 
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theVDude wrote:
quicksolver wrote:
As for the issue of the unsecured pieces, I think that pillowing is the best way to go (strictly from an "outsider's" perspective)

Or nonplanar cuts. AKA Make that puzzle curvy as heck! We like curvy lines!

Try making the cuts spherical. That sometimes helps me to see how to make a puzzle more stable.

Oh, and AWESOME puzzle idea!

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 Post subject: Re: Tridiminished icosahedron puzzle idea
PostPosted: Fri Jun 24, 2011 12:58 pm 
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Carl
I guess you're right. 3-cut puzzle was my initial idea. However, this puzzle would has 6 kinds of pieces.
Image
Green and gray pieces are 'stationary', dark gray and purple can be switched with each other . But two other kinds (if we don't consider shape-shifting moves) can't be. For example there are 15 'star-arms' pieces, but one can be placed only within 5 different positions. So these kind of piece splits into 3 groups. Same thing happens with red (on above image) pieces.
ImageImage.
I thought this would reduce number of achievable permutations and tried to add another cut. But it seems it won't make big difference in difficulty.

David Pitcher wrote:
If it's possible to use this pattern without having pieces fall out mid-turn

Yes, it is possible...
Image
Image
Image
...but it requires many small pieces.

As for non-planar cuts it could be really good idea but I must first try out few possibilities to find out which one would work best.

Krystian


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