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 Post subject: Is the SmaZ Dino Cylinder fudged?
PostPosted: Fri Nov 11, 2011 10:20 am 
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I think it is. Consider the eight small triangular pieces above & below each "eye" - these are the Dino Cube corners.
On the Dino Cube, they are normally hidden, and symmetric. On the Dino Cylinder, they are visible and asymmetric. They can each be independently rotated to 3 positions, and in two of those positions their curved sides push apart the overlying quarter-circle edge segments.

Here is an algorithm to twist the df triangular piece 120 degrees clockwise:

ur' df' dr' df dr ur uf df uf'

I have used the same notation as I did for the Mosaic cube:
http://robspuzzlepage.com/rearrangement.htm#mosaiccube

Here is a pic of this applied to all eight corners:
Attachment:
dino-cyl-fudging1.jpg
dino-cyl-fudging1.jpg [ 30.45 KiB | Viewed 720 times ]

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 Post subject: Re: Is the SmaZ Dino Cylinder fudged?
PostPosted: Fri Nov 11, 2011 10:42 am 
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This puzzle is not fudged. I think those gaps are caused by the fillets on the edges and you can notice them more when the center is turned since you can see through the gaps. I guess it would be possible for it to seem like gaps are present if there was some kind of flaw in the puzzle. Also I think by definition fudging would have to allow new moves.

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 Post subject: Re: Is the SmaZ Dino Cylinder fudged?
PostPosted: Fri Nov 11, 2011 3:19 pm 
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I agree that the definition of fudging entails changes to the puzzle that allow new moves.

In this case, think about the curved sides of the corner pieces. If the entire mechanism, particularly the circle-faced edge pieces, were extremely tight and geometrically precise, those curved corner piece edges would not fit between them.
In the actual puzzle, however, there is enough slack designed in to allow the corners to assume all possible orientations.
It is evident when you hold the puzzle in your hands after having applied a twist of the type I described, and trying to true up the circular face. You can't - it's always a bit uneven when an underlying corner is mis-oriented - and especially so when all four are.

I think the definition of fudging is something along the lines of "modifying piece shapes (generally reducing their size somewhat), or increasing the gaps between them, to allow piece permutations and/or orientations (i.e. moves) that would not be possible without such changes." Such modifications do not entail creating new cut lines.

I am thinking of the Tuttminx for example, where there is enough natural slack to allow inter-mixing of pieces that really weren't intended to do so - but without further design changes the moves become stiffer until they can no longer in practice be performed.
In the Dino Cylinder, the slack is enough that the moves never bind.

Now, SmaZ might not have been thinking about "fudging" when he designed it, but the end result is the same.

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 Post subject: Re: Is the SmaZ Dino Cylinder fudged?
PostPosted: Sat Nov 12, 2011 2:58 pm 
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I don't see how this would be fudging since it remains that only 120° moves can be made. You could use that same algorithm on a Dino Cube to turn the corner centers, but they would just be hidden.

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 Post subject: Re: Is the SmaZ Dino Cylinder fudged?
PostPosted: Sat Nov 12, 2011 3:37 pm 
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I agree with you that on the regular Dino, these moves can be made though the pieces are hidden. On the regular Dino there is no fudging needed since the hidden corner caps are symmetric and have no curved sides. Each of their 3 orientations is geometrically identical - the corner fits in its spot no matter which orientation it is in.

On the Dino Cylinder, however, only one orientation of a corner piece is "natural" - the other two are "strained" since it has two curved sides.

My point is that without the fudging (i.e. the slack between the quarter-circle edge pieces), the corner rotations on the Dino Cylinder would not be possible because of their curvature. It is the fudging that makes these moves possible.

In an "unfudged" Dino Cylinder, many moves would be precluded because the curved corner caps would not fit between the edge pieces in two out of their three orientations. So the fudging does result in "new" possible moves. The "unfudged" "natural" Dino Cylinder would have fewer possible moves than SmaZ' Dino Cylinder.

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