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 Post subject: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 11:25 am 
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Hello everyone.

Just quick question this time. Has this been made? If not, how hard in your opinion would it be to design?

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Krystian

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 11:37 am 
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Is it corner turning?

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 11:38 am 
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Is that a face turn Deep cut rhombic dodecahedron? If it is wouldn't that just be a shape mod of a 24-Cube aka Little Chop? Looks like this has too many pieces. So I assume this is either a corner turn Deep cut rhombic dodecahedron or an edge turn Deep cut rhombic dodecahedron . The corner turn version would be a shape mod of the 2x2x2/Skewb hybrid I think and I'm not sure if that has been built or not. I'm not even sure what the edge turn version would be...

Hmmm,
Carl

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 11:40 am 
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RubixFreakGreg wrote:
Is it corner turning?
I'm leaning toward edge turning looking at the pic some more.

Carl

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 11:58 am 
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It's edge-turning. It doesn't have too many pieces as it has one cut per axis. I can't make right now more renders so I'll try to describe it. The cut runs throught centers of edges of green face and then throught corners of blue and yellow faces. I hope it's clear.

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 12:53 pm 
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3 layer or deepest cut?

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 2:29 pm 
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It's a deep-cut edge turning rhombic dodecahedron, I'm almost sure. In other words a deep cut face turning icositetrahedron (is this the correct term? if not... well, the kite skewb shape)

I don't see why it shouldn't be possible, but it would probably be a beast to design and solve.

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Fri Apr 08, 2011 8:14 pm 
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Not sure how this thing turns, but I love the idea of a twisty puzzle with Unicursal Hexagrams cut into every face.

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Mon Apr 11, 2011 6:08 am 
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I made new renders. Also, there is strange thing about this puzzle that confuses me. I'll try to describe it. Here are pictures:

Solved
Image

After one turn
Image

Because of its shape, there are only possible 180 degrees turns.
In situation as above (2nd picture) the puzzle becomes 'locked' and works like one-layered Cheese (which is easy to solve). To unlock other possible moves we need back it to dodecahedral shape.
Let's look on it from above.

Image

Let A means turning 'ABF' half of the puzzle by 180 degrees, B - 'ABC' half and so on. After ACEFDF turn (from solved state) whole thing looks like this:

Image

The puzzle is 'unlocked' (rhombic dodecahedral shape) and a little scrambled. And here is my question about this locking. Does this puzzle need algorithms to be fully scrambled?
Maybe it's just me, but I didn't find a way to fully scramble it other than keeping it in original shape by using alg.

Krystian

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Mon Apr 11, 2011 8:01 am 
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If I get that right, this puzzle would have 12 throughgoing axes.
It would be a deepcut edgeturning rhombic dodecahedron.
A purely jumbling puzzle.


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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Mon Apr 11, 2011 9:32 am 
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Andreas Nortmann wrote:
If I get that right, this puzzle would have 12 throughgoing axes.
It would be a deepcut edgeturning rhombic dodecahedron.
A purely jumbling puzzle.

Yes. :)

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Mon Apr 11, 2011 11:42 pm 
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You think this puzzle jumbles ONLY at 180 degrees? :wink:
You, sir, have missed a few things :)

The core of this puzzle is properly called the Deltoidal Icositetrahedron according to Wikipedia (nice try Monopoly :wink: you got half of it!)

(on a side note: there is another page in Wikipedia called the Strombic Icositetrahedron which redirects to the same page... Am I the only one that finds this odd? Look at the URL after clicking this "alternate name")

According to my analysis, this core shape's geometry jumbles at some depth at each of the following rotations of any face:
(approximations in degrees)
34.0477323700
62.9643082106
101.5369590328*
122.8783495644
135.5846914028
180
(and then of course at 360 - any of the above values)

*this same angle occurs twice for two different slice interactions

Since you are looking at the deepcut version of the puzzle: ALL OF THESE JUMBLING MOVES ARE POSSIBLE!!!! :shock: (that's 12 positions, including the default 0° position, that a face can be in where at least one other move is possible!)

madartilect: Try to render some images of the puzzle after one of the above turns (on any of the rotation axes, they are all the same) and try to locate the cut that jumbles in each case 8-)

Disclaimer: It could be the case that several of these result in a dead end situation once completed, I haven't checked "playability", but at least one jumbling move at rotations throuch each of these angles from neutral is entirely possible!

And yes, Andreas has it right, I would say there are 24 potentially available moves around 12 axes (2 per axis). Then again, since this is a deepcut puzzle, only one move from each pair is needed to fully define the puzzle. Every single one of these moves can only stop at positions that puts the puzzle in a jumbled state.

As for how hard is it to solve? Depends on how many of these jumbling interactions produce interesting interactions. If the sequence you described above is the only one that doesn't dead end, i.e. more than just a few moves can be made, then it would only be moderately difficult. The more of these interactions pan out, the more ridiculously impossible it gets.

As for how hard is it to design? Theoretically possible, but highly implausible. A deep cut puzzle of this caliber would have 24 faces producing asymmetric interactions with one another. IMO only one puzzle has ever been made that is even comparable to the chaos of a mechanism that would be required to construct this thing and that is Drew's Chopasaurus. This puzzle would require at least double the number of internal parts as that, possibly more... (however, it wouldn't require as many pieces as a big chop theoretically needs so at least that's something :roll: )

Peace,
Matt Galla

PS: you could unbandage it in the same style as Oskar's Meteor Madness and end up with one devilishly hard puzzle with thousands (I think) of external pieces. I bet even schuma couldn't solve that one! :twisted: :lol:


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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Tue Apr 12, 2011 9:30 am 
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Allagem wrote:
You think this puzzle jumbles ONLY at 180 degrees? :wink:
You, sir, have missed a few things :)

Thanks for pointing this out.
Indeed, I've missed that somehow. :D

Allagem wrote:
madartilect: Try to render some images of the puzzle after one of the above turns (on any of the rotation axes, they are all the same) and try to locate the cut that jumbles in each case 8-)

Here they are:
~34 degrees turn (one jumbling cut)
Image
Image

~62 degrees turn (one jumbling cut)
Image
Image

~101 degrees turn (three jumbling cuts)
Image
Image
Image
Image

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Tue Apr 12, 2011 9:36 am 
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~122 degree turn (one jumbling cut)
Image
Image

~135 degree turn (two jumbling cuts)
Image
Image
Image

Allagem wrote:
Disclaimer: It could be the case that several of these result in a dead end situation once completed, I haven't checked "playability", but at least one jumbling move at rotations throuch each of these angles from neutral is entirely possible!

I'll check that out soon in free time.

Krystian

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 Post subject: Re: Deep cut rhombic dodecahedron
PostPosted: Tue Apr 12, 2011 7:03 pm 
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Allagem wrote:
The core of this puzzle is properly called the Deltoidal Icositetrahedron according to Wikipedia.


Actually, that is not true. It's something that I've been meaning to post on my ETRD (Edge-Turning Rhombic Dodecahedron) thread. People were saying that the Deltoidal Icositetrahedron (DI) is what you get if you cut off the edges of a Rhombic Dodecahedron in the same way you can get a Rhombic Dodecahedron by cutting off the edges of a cube.

Strangely, this does not produce the same shape as the one on Wikipedia (http://en.wikipedia.org/wiki/Deltoidal_icositetrahedron). The shape on Wikipedia is what you get if you take the dual of the Rhombicuboctahedron.

I have found (using Solidworks) that these two shapes are actually not the same! The easiest place to see the difference is in the vertices where 4 edges meet. There are two different types of 4-edge vertices. There are Type A vertices, where 4 long edges meet, and Type B vertices, where 2 long edges and 2 short edges meet. The angle to look at here is the angle between edges on opposite sides of the vertex; let's call the angle X.

In the picture below, the DI on the right is the one you get from a rhombicuboctahedron. On this shape, the angle is the same (225 degrees) on both types of 4-edge vertices. This was fantastic for the FTDI, since it resulted in the Type A and B corners being identical.

The DI on the left is the one you get from an RD. Notice that the angle between long edges (233 degrees) is not equal to the angle between the short edges (217 degrees). If I were to put cuts into this puzzle, the Type A corners would have 90 degree rotational symmetry, but the Type B corners will be somewhat "rectangular" having only 180 degree symmetry.
Attachment:
File comment: Left: Deltoidal Icositetrahedron from a Rhombic Dodecahedron. Right: Deltoidal Icositetrahedron from a Rhombicuboctahedron
Deltoidal Icositetrahedron Comparison.JPG
Deltoidal Icositetrahedron Comparison.JPG [ 182.64 KiB | Viewed 1730 times ]

What you have here, madartilect, is a true ETRD, since all the pieces rotate around axes that are perpendicular to the edges. This means that what I called my ETRD was technically not a true ETRD.

I recently tried to make a true ETRD (same depth as the one I made before), and it is very, very difficult to get a good mechanism. That's because the center pieces (those attached directly to the core by screws) are very far away from the points of the Type A corners, which makes it hard to get enough mechanism on the pieces that correspond to the Type A corners on the FTDI, while still leaving enough room to get a screw through the center piece.

After seeing how awesome this looks, though, I may have to give it another go.

-Eitan

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