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PostPosted: Sun Feb 18, 2007 1:57 pm 
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joey wrote:
qqwref wrote:
A simpler variation might be a puzzle where each axis turn turns half of the cube. It would look just like a Dino Cube, but be a lot harder to create, since each turn would turn 12 pieces...

Isn't that like his SuperX? http://twistypuzzles.com/forum/viewtopic.php?t=5948&highlight=


That puzzle is known as the "Little Chop" as discussed by Bram, and is much different than the SuperX. I have been "puzzling" over the mechanism for a while, but I have not cracked it yet. There is a virtual one at David Byrden's site. It is listed under "Odd Boxes".
http://byrden.com/puzzles/MainFrames.html

qqwref wrote:
Have you considered making a 5x5x5-like version? It would look like a 4x4x4 on each side, and have two axes of rotation on each of the axes. That would be pretty crazy as well.


This is possible (I think), but I have not even started thinking along those lines yet. I have many other ideas that are more complete and need to be made first.

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PostPosted: Sun Feb 18, 2007 2:14 pm 
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joey wrote:
qqwref wrote:
A simpler variation might be a puzzle where each axis turn turns half of the cube. It would look just like a Dino Cube, but be a lot harder to create, since each turn would turn 12 pieces...

Isn't that like his SuperX? http://twistypuzzles.com/forum/viewtopic.php?t=5948&highlight=


SuperX turns at the corners. Wouldn't what he's talking about turn at the edges?

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PostPosted: Sun Feb 18, 2007 2:28 pm 
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Puzzlemaster42 wrote:
Here is a fun picture of the parts prior to assembly.

I guess this is the case where a big original picture file is necessary to actually get the right appreciation! 8-)

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PostPosted: Sun Feb 18, 2007 3:00 pm 
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I've figured out two different (although somewhat related) mechanisms for the little chop. The problem is that the little chop is somewhat jumbleable, a property I didn't notice until after this thread started, and I haven't yet figured out how that interacts with my mechanisms, they might have some serious difficulties.


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PostPosted: Thu Feb 22, 2007 11:27 am 
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Puzzlemaster42 wrote:
Myke wrote:
Can it turn like a 2x2?


No.

This puzzle "looks" like a 2x2x2 and Skewb hybrid, but only the 12 edge centered axes turn.


Hmmm... it makes me wonder if 2x2x2 and/or Skewb type rotation could be added to the helicopter.

Great work... I'd LOVE to get both the Helocopter and the Super-X. Would you consider a package deal for both?

Carl


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PostPosted: Thu Feb 22, 2007 4:23 pm 
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Hmm that would be weird to have a combo of a 2x2, a skewb, and a helicopter cube.
But I don't know if that would be possible to be a custom mod.

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PostPosted: Thu Feb 22, 2007 4:37 pm 
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As funny as it sounds, puzzles can be made with magnetic center. It had been done before with 2x2x2. I have Japanese 2x2x2 ball that has magnetic core from 1981 and it moves pretty good, not what I would think before. This eliminates the need for an ingenious and complex mechanism that is difficult to make from scratch. The downside is that, well, it's a magnet, and that you can't really limit movements to only certain cuts though the puzzle. And of course not all puzzle can be made this way, but it's an easy solution for some.

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PostPosted: Mon Feb 26, 2007 3:26 am 
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i would really like a video of this puzzle and the super-x :D pleeeease (since that's most likely the closest i'll get to the real thing :))


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PostPosted: Mon Mar 12, 2007 8:35 pm 
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You should have a tutorial on how you made the super x and the helicopter cube... I would love to possibly make my own junky one... my dream cubes are a 6x6x6, super x, helicopter cube, dino cube, and a gigaminx... My goal is to someday own them all!!!

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PostPosted: Mon Mar 12, 2007 9:20 pm 
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Skate Addicti0n wrote:
You should have a tutorial on how you made the super x and the helicopter cube... I would love to possibly make my own junky one... my dream cubes are a 6x6x6, super x, helicopter cube, dino cube, and a gigaminx... My goal is to someday own them all!!!


He used rapid production along with CAD software and molding/casting material to make these puzzles. I'm not sure if he wants to reveal certain parts of his mechanisms.

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PostPosted: Tue Mar 13, 2007 5:38 pm 
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I think I know an idea of making one but I am not able to actually make the pieces... I could probably design it... I would first take a skewb cube and then manage to change the center peice so it is capable of turning and have the core attached with extra axises (Is that the plural of axis?) Also, this cube does turn like a skewb am I correct?

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PostPosted: Tue Mar 13, 2007 10:13 pm 
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Puzzlemaster42 wrote:
Myke wrote:
Can it turn like a 2x2?


No.

This puzzle "looks" like a 2x2x2 and Skewb hybrid, but only the 12 edge centered axes turn.

so yah... :(

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PostPosted: Wed Mar 14, 2007 8:17 am 
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Skate Addicti0n wrote:
Also, this cube does turn like a skewb am I correct?
No. It looks like it does, but doesn't.

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PostPosted: Wed Mar 14, 2007 7:01 pm 
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ok well then it makes it easier to solve and create... it would be extremely hard if it turned like it does now, like a skewb and like a 2x2x2... that owuld be so hard... I would prolly be able to make one except how to I get the peices... I could design it if i had the time...

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PostPosted: Thu Mar 15, 2007 2:36 pm 
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Bring that into production...NOW!

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PostPosted: Sat Jul 21, 2007 2:49 pm 
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isn't the axis like a megaminx's center? cept smaller...


i'm going to try to make an edge turning tetrahedron


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PostPosted: Sat Jul 21, 2007 8:51 pm 
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Please stop bumping old topics.

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PostPosted: Mon Jul 23, 2007 8:00 pm 
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Ranaakamarth wrote:
isn't the axis like a megaminx's center? cept smaller...


i'm going to try to make an edge turning tetrahedron


The core has the geonmetry of a Rhombic Dodecahedron, and is not the same as the dodecahedron in the Megaminx. The center of this puzzle is a unique custom part.

Good luck on the edge turning Tetrahedron. It looks like an interesting puzzle.

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PostPosted: Tue Jul 24, 2007 6:20 am 
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Many thanks for bumping this topic up -- I would have missed it otherwise! :lol:
It's a lovely piece of work.


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PostPosted: Tue Jul 24, 2007 8:40 am 
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I can't see anything wrong with bringing back old posts: I was surprised how many posts I have missed and was glad I had a chance to read them when they turned up the second time round!
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PostPosted: Tue Jul 24, 2007 12:08 pm 
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I'm also glad this was bumped. What an incredible design and build!

:shock:


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PostPosted: Fri Jul 27, 2007 5:41 pm 
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I don't know how serious the idea was about an edge-turning octahedron but I experimented with how this would be built a while back. I am nowhere near skilled enough to make it, but I bet someone here could realise it. I came up with a series of sketches of how it could be built and I offer them as a start to anyone willing to take up the challenge.

Hmm... Let's see if I can post images correctly...


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PostPosted: Fri Jul 27, 2007 5:42 pm 
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So this is the core... its the same as the helicopter cube I think... I think it's called a rhombic dodecahdron?


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PostPosted: Fri Jul 27, 2007 5:44 pm 
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Ok so next you would add these tips that would just spin around


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PostPosted: Fri Jul 27, 2007 5:45 pm 
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After you've connected half of these tips it would look something like this


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PostPosted: Fri Jul 27, 2007 5:48 pm 
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Then this is where it becomes too difficult for me. All of the remaining peices have to be connected somehow to the pieces shaded yellow, but I'm not sure how to do it. I know there needs to be some sort of groove system with interlocking tabs and such


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PostPosted: Fri Jul 27, 2007 5:49 pm 
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So if you can find some way to connect them then you would continue to connect more of this next piece all over the puzzle


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PostPosted: Fri Jul 27, 2007 5:50 pm 
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Then a new piece would fill in the gap here


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PostPosted: Fri Jul 27, 2007 5:51 pm 
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And the same piece would fill all of these gaps


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PostPosted: Fri Jul 27, 2007 5:52 pm 
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And then this piece...


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PostPosted: Fri Jul 27, 2007 5:53 pm 
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...would fill in practically the rest of the puzzle


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PostPosted: Fri Jul 27, 2007 5:53 pm 
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And finally the point


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PostPosted: Fri Jul 27, 2007 5:54 pm 
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A few more...


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PostPosted: Fri Jul 27, 2007 5:58 pm 
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And there you go, an edge-turning octahedron. As you can see the only planning missing is how to keep the pieces connected together so if anyone, ANYONE can do that, then please bring this dream to life

(Just FWI the colors are just to distinguish the different pieces apart, not a cloring scheme or anything. All similar pieces are the same color)


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PostPosted: Fri Jul 27, 2007 8:03 pm 
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The yellow and green pieces correspond to the corner and face pieces of the Helicopter Cube. The blue and purple pieces are additional pieces added to the puzzle between the face pieces. The following sphere applet links show the difference between the two puzzles.

Helicopter Cube
[url=http://www.geocities.com/jaapsch/puzzles/sphere.htm?red=189&symred=4&angle=9,58,5]E.T. Octahedron
[/url]
It may be possible to put the additional pieces in between the existing ones, but I don't know if there will be enough room.



By the way, what program are you using to make the pictures?

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PostPosted: Sat Jul 28, 2007 2:45 pm 
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It's a simple 3D program called Cabri 3D

And yes I thought the Helicopter Cube had the same core and therefore corresponding pieces, but do you think you could get the additional pieces to function correctly? This is just an idea, but maybe if you were able to get the Helicopter Cube pieces to work, then why not the others? I think you should go for it, but it's up to you.

PS: Yes that sphere thing from Jaap's site perfectly describes the relationship, I've never found that before!


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PostPosted: Wed Aug 01, 2007 7:10 pm 
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i said tetrahedron not octahedron.


I said i was just thinking about it...

I still don't have any puzzle building materials to do it yet.

I only get $7 per grass cut... and i keep blowing all my cash on stuff like dogics and skewbs....

i'll get around to buying some epoxies and stuff sooner or later. Maybe when i get a decent job.


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 Post subject: Re:
PostPosted: Sat May 10, 2008 3:57 am 
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Sorry to reply to an old thread, but...

Darren Grewe wrote:
Bram wrote:
Another one which *might* work is to take the truncated tetrahedron and split the hexagons into six triangles each, and have rotations around the edges which are shared between hexagons. Yet another one is to take the truncated octahedron and split the hexagons into six triangles and the squares into four triangles. Both of those might fail completely though, I have a lot of trouble visualizing them.


Vall me crazy but don't those puzzles allready exist right now?!?!?!?!?!

First link is a Tetraminx

http://twistypuzzles.com/cgi-bin/puzzle.cgi?pid=548

Second link is a Christoph's Magic Jewel

http://twistypuzzles.com/cgi-bin/puzzle.cgi?pid=641

Please correct me if I am wrong.


Then Bram replied
Bram wrote:
Uh, yeah, I edited the comment to say that I was totally wrong on those.


Hang on Bram, your ideas were just fine, and not at all the ones Darren mentions. Those ones have rotation around different axes (3-fold and 4-fold respectively), whereas Bram is suggesting rotation around the 2-fold symmetry axes. The faces get divided into parts the same either way, except that in Bram's truncated octahedron the squares are also split up, whereas they are not in the Magic Jewel.

Thinking some more, the edge-rotated truncated tetrahedron (or indeed tetrahedron) would actually be a 3x3x3 mod. Has no one made that yet? (Probably have). The "jumbleable" aspect would occur at 90 degrees, the 2-fold axes really being sub-symmetries of the 4-fold axes of a 3x3x3 cube.

Rob.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Tue May 13, 2008 6:40 pm 
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(swapping back into brain ... ouch ... the pain ...)

Gee, I'm not sure why I thought I was wrong on the truncated tetrahedron. You're wrong about the mechanism though - it isn't a particular n-fold symmetry, it's rotation about the vertices, which have no rotational symmetry at all. The overall shape is that there are hexagonal pyramids of a funny height on each of the hexagonal faces, such that two edges of one pyramid, two edges of an adjacent pyramid, and the edge of the shared triangular face all lie in the same plane. Then you can rotate about that plane and, uh, jumble it. There are three kinds of pieces - the triangular faces, the pieces which straddle two pyramids, and the pieces which are on a pyramid and initially border a triangle, which are obviously exactly half the size of the other ones, at least the visible portion of them is. The edges on it are kind of sharp though, so it might be annoying to play with.

The truncated octahedron is a similar story, only in addition to pyramids on the hexagonal faces there are diagonal cuts on the square faces. A whole lot more shallow little pieces on that one, but it does technically exist.

I'm actively working on one of the designs I mentioned earlier in this thread. Not sure if anybody understands any of this babbling though.

I'm also starting to think that the subset of the shrapnel ball which rotates on five axis and is jumbleable might have a semi-reasonable mechanism. That one seriously hurts my brain though.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Wed May 14, 2008 3:21 am 
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Bram wrote:
You're wrong about the mechanism though - it isn't a particular n-fold symmetry, it's rotation about the vertices, which have no rotational symmetry at all. The overall shape is that there are hexagonal pyramids of a funny height on each of the hexagonal faces, such that two edges of one pyramid, two edges of an adjacent pyramid, and the edge of the shared triangular face all lie in the same plane. Then you can rotate about that plane and, uh, jumble it.


Oh, those could work, but they're not what you were describing earlier. You wrote "split the hexagons into six triangles each, and have rotations around the edges which are shared between hexagons". That would produce puzzles visually the same as those links to existing puzzles, but operating differently.

As I mentioned, the edge-turning tetrahedron (or truncated tet) would just be a 3x3x3 mod, except that 4 of the 8 corner pieces would need to be gotten rid of or filed down to small bumps that can be ignored.

Here's a pic of what you're describing now (I think)
Image

And here it is without the extra pyramids:
Image

I think those would jumble, although it's a bit hard to visualise whether you'd be able to do more than 1 or 2 moves.

Rob.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Wed May 14, 2008 4:34 am 
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Quote:
As I mentioned, the edge-turning tetrahedron (or truncated tet) would just be a 3x3x3 mod


Correct, the Mastermorphix.

On a related note, can somebody please *clearly* define what "jumbleable" is supposed to mean? Thanks:)

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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Wed May 14, 2008 7:02 am 
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To, as the puzzle is scrambled, not retain the same shape or likeness of the puzzle in its solved state.

Now my question is, what if the puzzle only changes minutely? For example the half-truncated cube? or the extended 3x3x4? Would you call that "jumblable"


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Wed May 14, 2008 9:10 am 
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The only "jumblable" puzzle created so far is the Helicopter Cube [Bevel Cube, Half Chop]. The term "jumblable" refers to the ability of the puzzle to make moves that are not expected. In this case, the expected moves are 180 degrees turns about an edge centered axis. The unexpected move occurs when one edge is turned 70.53 degrees, causing it's cuts to line up with the adjoining edge.

By making only 180 degrees turns, the pieces follow certain rules. For example, the face [center] pieces follow 4 orbits of 6 pieces each, but when jumblable moves are applied, the face pieces can be swapped between orbits. This allows positions to be reached that are unobtainable by only 180 degrees turns. It adds an optional level of difficulty in solving the puzzle.

I posted 2 pictures on the first page of this thread showing why the mechanism behaves in this way. It is a bit like a circle puzzle, but with multiple circles around a sphere.

The only other puzzle that I am certain is Jumblable (normal turns and unexpected turns) is the dodecahedral version of the Helicopter Cube, shown below (some cut planes are not shown). There are most likely entire families of puzzles like this, but I have not explored them yet...


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Wed May 14, 2008 2:04 pm 
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Thanks, that's what I thought, but with the terminology not clearly defined I have been a bit unsure more than once :)

However, with that statement of what "jumbleable" is supposed to be, it makes it fairly straightforward to create a jumbleable puzzle--the slices that the mechanism defines simply needs to based on a rhombus, much like the Helicopter Cube. Thus, putting a new shape around this mechanism (like the above octahedron puzzle, for example) will always preserve the jumble feature.

Finally, I don't think you'll be able to achieve this particular feature with less than 12 axis, and the next "opportunity" requires 30 axis--the dodecahedron puzzle sketched above, that is.

Gotta run!

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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Thu May 15, 2008 1:38 am 
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I think the term jumbleable is a little under-defined. The tetrahedral equivalent of the helicopter cube is probably the simple pyramorphix (edge-based turning axes, slicing to half-way down adjoining edges), and the Mastermorphix discussed above is similar. In both cases you would "expect" to twist through 180 degrees to maintain the tetrahedral shape, but can also twist through 90 degrees and alter the shape. Does this make it jumbleable? I don't think it should fall into the same category.

Maybe the difference is that jumbling can also lead to jamming. Also, twists happen at angles that don't factor into 360 an integral number of times.

Rob.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Thu May 15, 2008 1:41 am 
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the.drizzle wrote:
Quote:
As I mentioned, the edge-turning tetrahedron (or truncated tet) would just be a 3x3x3 mod


Correct, the Mastermorphix.


Oh, cool. The curvature is required because otherwise some method is needed to get rid of 4 of the 8 corner pieces altogether. It looks great, but I guess I'm a traditionalist, and would like to see a flat version :)

Rob.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Thu May 15, 2008 1:49 am 
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Robert, the curved version is kind of a fashion puzzle. 8-) Traditionally it's been always made flat.

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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Thu May 15, 2008 10:44 pm 
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Location: Marin, CA
Robert: yes, that's exactly what I meant! Thanks for the illustration.

the.drizzle, there is in fact a 6-axis jumble puzzle, but you have to work out my babbling early in this thread to figure out what it is :-)

Robert: Bandage puzzles can also have moves which are blocked, but that doesn't make them jumbleable. How about if we define jumbleability as involving rotations which aren't a rational fraction of 360 degrees?

I'd like to point out that deeper cut jumble puzzles are possible, but they tend to jam a whole lot more.


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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Thu May 15, 2008 11:43 pm 
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That's not really a suitable definition to me because we can't ensure that the jumbling angle will never be a multiple of 360 degrees. Personally I would define a jumbleable puzzle as a puzzle which has the same possible turns (at the same angles) no matter what moves have been done on it (assuming you can't do moves which prevent adjacent axes from turning). I'd call that 3x3x5 that was sold a while ago jumbleable by this definition, since if you mix up the 3x3x3 part the split-layer turns are prevented unless you line the right pieces up - and I would say that many bandaged puzzles can be jumbled in the sense that the allowed turns and the relative positions of the types of pieces are not fixed.

This might be a bit more general than what your intuitive definition is, but I think it's an important distinction to make between puzzles where the possible turns and the 'shape' of the puzzle depend on the state the puzzle is in (such as the Bevel Cube and various bandaged puzzles) and puzzles which have the same shape and the same possible turns in every scrambled position. Perhaps mathematically you could say a puzzle is non-jumbleable if its positions form a group, although I'm not entirely sure if this holds for the Helicopter Cube.

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 Post subject: Re: New Puzzle: Helicopter Cube
PostPosted: Fri May 16, 2008 1:22 am 
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qqwref, Whether there's an angle which isn't a rational multiple of 360 degrees which causes another slice to be possible is a completely well defined mathematical conjecture, and one which for the helicopter/bevel cube is clearly true. Arguing otherwise is like claiming it's possible to trisect an angle with a compass and straightedge.


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