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 Post subject: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 9:20 am 
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Hi Twisty Puzzles fans,

With all the discussions on jumbling going on, I thought that some of you would appreciate seeing a more doctrinaire puzzle from me. Illegal Cube is based on the geometry of a Pentagonal Prism. As you know, a classic pentagonal-prism twisty puzzle has square sides that can only turn in steps of 180 degrees. Illegal Cube is different from that.

Jason Smith came up with the concept of turning a square face of a pentagonal prism by 90 degrees. He added some extra cuts such that all square and pentagonal faces can turn again. The result is a versatile prims that has 90 degrees turns. Jason's concept jumbles, as infinitely more cuts are needed to fully unbandage his puzzle.

Like Jason's concept, Illegal Cube's square faces can make 90-degrees turns. However, I fudged the edges and corners such that all 15 edges and 10 corners are identical, and that they have the symmetries of regular Rubik's Cube edges and corners. This can be achieved by designing some crevices between the pieces. During each 90-degrees turn, the corners are reoriented a bit, such that the puzzle returns to its original shape after each turn.

I believe it was Bram Cohen, who introduced the term "fudging" for this type of movements. A proper definition of "fudging" would be welcomed. What do you think, is this fudged Illegal Cube a doctrinaire twisty puzzle?

Watch the YouTube video.
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Enjoy!

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Attachment:
Illegal Cube - prototype - view 1.jpg
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Illegal Cube - prototype - view 2.jpg
Illegal Cube - prototype - view 2.jpg [ 41.07 KiB | Viewed 6424 times ]

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Illegal Cube - prototype - view 3.jpg
Illegal Cube - prototype - view 3.jpg [ 39.7 KiB | Viewed 6424 times ]

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Illegal Cube - prototype - view 4.jpg
Illegal Cube - prototype - view 4.jpg [ 44.51 KiB | Viewed 6424 times ]

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Last edited by Oskar on Sat Jul 03, 2010 12:06 pm, edited 2 times in total.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 9:23 am 
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OMG CALL THE COPS

amazing puzzle oskar

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 9:26 am 
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Fudging: the slight changing of shape, addition of gaps, or introduction of other minor irregularities to a Twisty Puzzle that allows for the changing of functionality of the puzzle.

At first when I saw this I thought that it was nothing special and thought that the Fudging was odd but now I see that 90 degree turns are possible and my ideas have changed. Nice idea!

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 10:02 am 
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Very sneaky. Still not completely sure how this works. It seems like there should be a lot of play in the pieces but the video shows that it's quite tight. I wonder if it's possible to make an illegal Tuttminx by the same method.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 10:39 am 
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Great puzzle Oskar!

I had a similar idea, only I was thinking of using triangular prism geometry. I had a rough idea for the mechanism, but since I couldn't figure out a way around the problem of how to shape the outside pieces I had pretty much given up on the idea, though I maybe didn't put in enough thought. Fudging seems to be a really cool solution to the problem. Trust you to figure out how to make the unusual geometry work!

Fudging seems to be: changing the ouward appearance of the pieces of a puzzle such that adjacent pieces don't lie flush with each other, to allow for unusual functionality of the puzzle which cannot be achieved with the usual geometry.

I'm not sure of your definition of a doctrinaire puzzle, so I don't know if this matches the definition or not. It doesn't seem to jumble due to the fudging, so I would say it maybe is doctrinaire, but I'll leave the decision to people like you, Bram and others round here who are more expert on the definitions.

Matt


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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 11:18 am 
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Really amazing puzzle :mrgreen: I would love to try to solve this.
"Fudging" could be the addition of voids in a puzzle mechanism allowing new ways of movement.
This is one of my favorite puzzles from you, great job :D

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 11:21 am 
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Nice idea. Please don't call your next puzzle "The Knock-off Cube" though.

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Last edited by Tony Fisher on Sat Jul 03, 2010 12:25 pm, edited 1 time in total.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 11:29 am 
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Great puzzle as always. I don't really like the looks of the final product, but as it is (one of) the only solution to make this concept work, I don't mind it. (who am I to mind it anyway??)

I don't think it would be too hard to solve, just like most 3x3x3 solutions, but with some modified algorithms for the last side.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 11:33 am 
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Oscar, your asking for trouble, some people don't like to see our sacred laws (of physics) broken like this. :shock:

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 12:13 pm 
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Incredible Oskar, when I saw that on ShapeWays, I thought it was just a Pentagonal Prism. But this... wow!

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 1:31 pm 
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You know that age old question... Why did the 3x3x3 cross the road?

Well it looks like we still don't have an answer to that question but this does look like the answer to what happens when the 3x3x3 doesn't make it.

I think the perfect name for this puzzle is The Roadkill 3x3x3. It's all bloated and stretching at the seams and looks like its about to pop. This may be the first twisty puzzle where I'm not so eager to see what's on the inside. LOL!!

Did I mention I have an odd sense of humor? Poor 3x3x3... I hope it didn't suffer too long.

Carl

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 2:42 pm 
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I think this is definitely a doctrinaire puzzle. It's also a very cool puzzle!

I have a suggestion for the stickers, though. Perhaps it's just me, but the stickers look kind of messy. It's probably because of the fudging, since that causes odd gaps that show up on the external puzzle. Since those gaps are wedge-shaped, the stickers look like they are misaligned when I am sure they are not (as I know that Oskar is good at making puzzles :P ). Perhaps instead, you could mirror the wedge-shaped gaps in the shapes of the stickers, causing the gaps to look more rectangular from a distance.

What do you think?

-π (Eitan)

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 2:53 pm 
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I've been wondering why you call it "illegal" since I saw your Shapeways page about it. Now that I know why, I am amazed! :D

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 6:05 pm 
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So... does the fact that there are two pentagonal faces introduce any parity to solving?


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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 6:37 pm 
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Oskar wrote:
Jason Smith came up with the concept of turning a square face of a pentagonal prism by 90 degrees. He added some extra cuts such that all square and pentagonal faces can turn again. The result is a versatile prims that has 90 degrees turns. Jason's concept jumbles, as infinitely more cuts are needed to fully unbandage his puzzle.


Is Jason's concept public? I'd like to compare an image of his idea with this puzzle.

Oskar wrote:
I believe it was Bram Cohen, who introduced the term "fudging" for this type of movements. A proper definition of "fudging" would be welcomed. What do you think, is this fudged Illegal Cube a doctrinaire twisty puzzle?


I'd say yes, its a doctrinaire puzzle. But I don't think I'd call it a pure twisty puzzle. Since its doctrinaire it doesn't jumble. It doesn't appear to have slidey pieces either. So I'd say you just broke the universe again. Let me guess... we now have twisty moves, jumbling moves, slidey moves, and fudging moves?

Fudging = a twisty move that almost works so Oskar works his magic and makes it work.

I don't know... since some of the slidey moves require voids and this fudging method requires some voids maybe the two could be combined.

Carl

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 6:56 pm 
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I think I saw some Xen invaders today... better call Gordan Freeman.

Please, please, stop breaking the universe. The covenant are not forgiving.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 9:08 pm 
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wwwmwww wrote:
I don't know... since some of the slidey moves require voids and this fudging method requires some voids maybe the two could be combined.


I don't think so. For a slidey puzzle, you need voids the size of one normal piece. Here, the voids are just big enough to allow the otherwise "illegal" turns. Oskar, you have my full permission to continue breaking the universe once a week.

-Eitan

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 03, 2010 11:40 pm 
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Fudging is a way of making a puzzle work. It is not how the pieces move so it is not sliding. I think any design with fudging could be made without it as well. Does this puzzle have any internal pieces? If so then I don't know a thing about fudging.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sun Jul 04, 2010 12:08 am 
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When i first saw a pentagonal prism i assumed it turned like this and was a little disappoint when i saw it didn't. Glad someone made one how i imagined them.
Oskar wrote:
Jason's concept jumbles, as infinitely more cuts are needed to fully unbandage his puzzle.
The link provided doesn't show Jason's concept, nor have i ever heard anything of it before,i was wondering if there is a thread on it or if it was just a concept never discussed?
oops i should have read the thread more thoroughly wwwmwww asked the same thing already.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sun Jul 04, 2010 9:00 am 
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Quote:
Jason's concept jumbles, as infinitely more cuts are needed to fully unbandage his puzzle

So that means that the puzzle has restrictions when 90° moves are used right? I imagine this to be really hard to solve. On a helicopter cube for example, you see the changed shape and with some experience can get it back to cube stage. But on this puzzle you don't see the changed shape, so analysing the corners' orientations or someting will be needed.

I am really glad you wrote that sentence you quoted above. I haven't read this information before anywhere on this forum for some reason, since I guess it has been mentioned in some thread.
I once tried to create a helicopter sphere that wouldn't have restrictions and I just couldn't finish it. I eventually got confused by millions of lines and angles and my programm wouldn't go any further either.
I guess the reason is that It doesn't take a certain huge number of cuts but infinetly many.

This puzzle is an amazing construction as always. But you must forgive me when I say that I would never want to have one since it would drive me insane.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sun Jul 04, 2010 3:02 pm 
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This puzzle jumbles? It didn't look like it had any restricted moves to it. I thought you could solve it the same way as a Rubik's Cube.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sun Jul 04, 2010 3:27 pm 
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yould it not be solved slightly like 5x5 centres? or am i barking up the wrong tree?

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sun Jul 04, 2010 3:28 pm 
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SEBUVER wrote:
This puzzle jumbles?


They are talking about Jason's concept puzzle which as far as I know hasn't been shown yet. Not the puzzle Oskar presents above.

Carl

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Mon Jul 05, 2010 5:50 pm 
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GuiltyBystander wrote:
Very sneaky. Still not completely sure how this works. It seems like there should be a lot of play in the pieces but the video shows that it's quite tight. I wonder if it's possible to make an illegal Tuttminx by the same method.


I dunno. I think it would make it easier.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Mon Jul 05, 2010 7:18 pm 
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Hmm, you're probably right. Though I wouldn't mind testing your theory if I had a Tuttminx :D

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Tue Jul 06, 2010 1:38 am 
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Aaron Williams wrote:
could it not be solved slightly like 5x5x5 centres? or am i barking up the wrong tree?
I would solve it more like a megaminx missing the middle. As in do the equivalent of megaminx star then F2L then go straight onto megaminx last layer.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Wed Jul 07, 2010 12:20 am 
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Wow, great work Oskar! As usual...

I think fudged designs are quite difficult to CAD.

For everyone who asked about the puzzle that inspired Oskar to create his version, I haven't shown it publicly yet. But I'll post a couple of images below! :) I'd like to finish up a working sample soon, but the Versatile Prism is part of the pile of carnage in my life created by the Helicopter Cube.

I called it the Versatile Prism because it's able to do moves other pentagonal prisms only dream about. 90 degree face turns! Other pent prisms wish they had that on their resume's!

The idea for a fudged version came up in a conversation with Bram in my garage about whether a fudged version might be more elegant than my jumbling version. We decided that the jumbling version offers quite a lot as a puzzle so I decided to finish it first. I'm thrilled Oskar picked up the concept with fudging and put his own unique style into it. It looks great. I'm really looking forward to seeing this in a few days!

I hope these images help to show how the jumbling version will work.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Wed Jul 07, 2010 12:48 am 
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io wrote:
For everyone who asked about the puzzle that inspired Oskar to create his version, I haven't shown it publicly yet. But I'll post a couple of images below!
Very interesting. I like how these two puzzles turn in an almost identical way and yet would be very different to solve.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Wed Jul 07, 2010 1:22 am 
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Elwyn wrote:
io wrote:
For everyone who asked about the puzzle that inspired Oskar to create his version, I haven't shown it publicly yet. But I'll post a couple of images below!
Very interesting. I like how these two puzzles turn in an almost identical way and yet would be very different to solve.

I agree. Oskar's could be solved almost like a layer by layer 3x3x3 while Jason's would be an all new solution.

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Thu Jul 08, 2010 3:47 pm 
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GuiltyBystander wrote:
Hmm, you're probably right. Though I wouldn't mind testing your theory if I had a Tuttminx :D


Who wouldn't? :D

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Fri Jul 09, 2010 10:43 am 
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Congrats, Oskar, you have violated the laws of geometry... Now the Universe is going to explode :shock:

As for your question as to whether or not this puzzle could be classified as "doctrinaire", I believe that it can. While the Illegal Cube does not hold up to the rigid geometric confines of a classic twistypuzzle, it very definitely follows the definition of a sequential motion puzzle. There are three part types: centers, corners, and edges. Centers can be classified as either square or pentagon. A rotation by one of the pentagonal faces permutes two 5-cycles, one of 5 edges and one of 5 corners. Likewise, a rotation by one of the square faces permutes two 4 cycles of edges and corners, respectively. The overall type, position, and shape of all pieces is preserved after every move, meaning it cannot jumble. The overall group-cycles are clearly well-defined as in a normal puzzle.

I believe that this is a case in which each additional cut is used to "unbandage" the rigid prentagonal pizm puzzle, in such a way that the "infinite dust" only occurs in the crevasses between the pieces without totally disintegrating the main parts. Io's "jumbling" version represe3nts only the first such iteration. The thin wedge shaped area eventually gets sliced to dust after repeated iterations, leaving the smoothly rounded edges and corners in their wake. With good, tight springs, the puzzle holds together. :solved:

It is a doctrinaire twistypuzzle with non-doctrinaire geometry. :mrgreen:

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 Post subject: Re: Illegal Cube by OSKAR
PostPosted: Sat Jul 10, 2010 2:59 pm 
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You sir deserve 100 internets

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