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 Post subject: MultiCubes (a sub group of the Circle Cubes)
PostPosted: Sat Sep 19, 2009 12:49 pm 
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The 4×4×4+2×2×2 Cube has been built. And is now being mass produced as Crazy 4×4×4 cube I. It's available here. And here is a video.

So not to derail the other threads I wanted to talk about the other [s]Super[/s] Super Cubes. I just realized that I think they are potentially buildable in the form of what's being called the family of circle cubes. Here is a sketch I made of what I think the 5×5×5+3×3×3 cube and the 6×6×6+4×4×4+2×2×2 cube could look like.

Image

The 5×5×5+3×3×3 cube doesn't need the 5×5×5 face centers as they are always the same color of the underlying 3×3×3 face centers, so no need to show that color twice.

The 6×6×6+4×4×4+2×2×2 cube gets a bit more complicated but also appears doable. The red pieces, inner circle, show you the face of the 2×2×2 cube. The blue pieces, now a ring instead of a solid circle, shows you the face of the 4×4×4 cube. And the white pieces, the outer area and a discreet ring, shows you the face of the 6×6×6 cube. Note, without the seperate white ring you don't have the centers of the 6×6×6 cube represented. Unlike the 5×5×5+3×3×3 cube, here the state of the underlying face centers don't necessarily represent the state of the outer face centers.

So now that we've seen the first [s]Super[/s] Super Cube, the 4×4×4+2×2×2 Cube progress all the way to mass production (which makes me ecstatic) any chance we'll see any more [s]Super[/s] Super Cubes in the near future. I'm actually a bit surprised the 5×5×5+3×3×3 cube hasn't already made an appearance. If it has and I've missed it could someone please post a link.

Thanks,
Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Sep 19, 2009 4:12 pm 
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The 5x5 + 3x3 won't need two centers for a regular super-supercube, but it would for a true super-super-supercube.


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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Sep 19, 2009 4:47 pm 
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Jared wrote:
The 5x5 + 3x3 won't need two centers for a regular super-supercube, but it would for a true super-super-supercube.


Agreed. That is why I have the [s] [/s] around the first super. In some forums that is used to strike out text. I'm not sure how to do that here. But seeing as Crazy 4×4×4 cube I isn't a super super cube we are talking about the regular super cubes here. Hmmm... I just noticed you had 3 supers... what does the 3rd one mean?

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Sep 19, 2009 5:14 pm 
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I see a problem... with normal circle cubes, 2x2x2, 3x3x3, and 4x4x4 the center circles are fixed and cannot turn with the outer layer... as is the case with the super supercube 4x4x4/2x2x2.
With the super-super 6x6, you could not simply make both centers fixed like the others, because then the 2x2 portion of it would not be able to scramble independently of the 4x4 part.
I believe you'd have to fix the 2x2 centers to the 3rd and 4th layers and the 4x4 part to the 2nd and 4th layers respectively...

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 12:22 am 
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wwwmwww wrote:
Hmmm... I just noticed you had 3 supers... what does the 3rd one mean?


I guess I was confused by your notation. I was thinking:

Supercube: regular cube with stickers which force 1 solution.
Super-supercube: cube-in-cube with regular stickers.
Super-super-supercube: cube in cube with super stickers.

I think we need better terminology though - perhaps "multicube" instead of "super-supercube" would be better. That way it would be:

Supercube: same as before.
Multicube: cube-in-cube with regular stickers.
Supermulticube: multicube with super stickers.


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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 11:22 am 
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Jared wrote:
I think we need better terminology though - perhaps "multicube" instead of "super-supercube" would be better. That way it would be:

Supercube: same as before.
Multicube: cube-in-cube with regular stickers.
Supermulticube: multicube with super stickers.
Agreed...

I've asked about this nomenclature twice before, here and here. And so far the closest thing I've found is the CubixPlayer2 program made by Per which simulates a Super Cube with all the possible smaller Super Cubes that it incases. And it calls these Super Super Cubes so I was wanting a way of specifing the second super without keeping the meaning of the first, so I tried to cross it out. I like the name Multicube but I also don't want to make up new names if there are already standards in place. In this case it seems there should already be an accepted name... somewhere. I just haven't come across it. Then again I remember back in the 90's (pronounced nineties) wondering what the next decade would be called. I can type 00's but I still don't know what to call that. Same goes for the 10's? I would have thought that problem would have been addressed a long long time ago. It seems centuries just don't get the ball rolling until they're in there twenties.

Anyways... if Multicube isn't already taken for something else and there is some agreement here that there isn't already a standard name in place that covers these I'm more then happy to use it. In fact there is another idea in my head that I'd like to talk about and I'm thinking of calling that a Multidodecahedron.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 11:36 am 
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elijah wrote:
I see a problem... with normal circle cubes, 2x2x2, 3x3x3, and 4x4x4 the center circles are fixed and cannot turn with the outer layer... as is the case with the super supercube 4x4x4/2x2x2.
With the super-super 6x6, you could not simply make both centers fixed like the others, because then the 2x2 portion of it would not be able to scramble independently of the 4x4 part.
I believe you'd have to fix the 2x2 centers to the 3rd and 4th layers and the 4x4 part to the 2nd and 4th layers respectively...
I don't know a mechanism yet for actually building this puzzle... if that is the problem you see. But yes you describe it as I envision it. Assume the picture above is the top view of the 6×6×6 Multicube. When the top layer is turned just the white pieces would move. When the 2nd layer is turned just the blue pieces would move. And when the 3rd layer is turned just the red pieces would move. I'd still think of this as a type of circle cube too... just a fair bit more complicated then I've seen before. The red and blue pieces do not turn independantly or with the outer layer as is the case with other circle cubes.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 11:52 am 
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The 6x6 example, in theory, shouldn't be too hard. Following the example set by the 4x4 + 2x2, you would build a 2x2 cube into a core, build a 4x4 around that, and a 6x6 around the 4x4. It might not be correctly proportioned but it might work. The only problem is getting the inner circle between the rings on each face to be connected to the 6x6 but not to everything else.


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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 12:08 pm 
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I agree, I was just thinking about that, somehow the inner ring that was connected to the 6x6 itself would have to internally connect... in this case I think the rings would have to be "floating" pieces to make the puzzle function correctly.
Also, when you get above the 6x6 cube, it gets much much more complicated, integrating pillowing, more floating pieces and even more rings connected to the various layers. I would not bet on the 7x7+ multicubes being very stable.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 1:30 pm 
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Jared wrote:
The only problem is getting the inner circle between the rings on each face to be connected to the 6x6 but not to everything else.
I too see that as the biggest problem. I'm not sure its the only one.

elijah wrote:
I agree, I was just thinking about that, somehow the inner ring that was connected to the 6x6 itself would have to internally connect... in this case I think the rings would have to be "floating" pieces to make the puzzle function correctly.
What if the inner white ring was connected to the 6×6×6 via magnets. There wouldn't be a physical connection in the way of the blue pieces so it should still be possible to connect it to the 2nd layer. And as the red pieces are inside the white ring I think they too would have room for a physical connection. If magnets are a no-no, then you could have broken bridges that went over the blue pieces that would lock the inner white ring in position relative to the outer white pieces. Personally... I'd perfer magnets over that option. And I'm still not sure some form of inner connection isn't possible. I think it might be possible to have the inner white ring connected to the outer white pieces through some gears hidden in the blue pieces themselves.

And I agree expecting a 7×7×7 multicube to be made anytime soon is pushing it. I may be pushing it with the 6×6×6 multicube. But I view the 5×5×5 multicube as something that could turn up any day now so I'm wanting to push things just a bit.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 1:44 pm 
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Even with magnets, you'd still need surfaces touching and therefore the blue pieces would be floating.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 3:19 pm 
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elijah wrote:
Even with magnets, you'd still need surfaces touching and therefore the blue pieces would be floating.
Well the magnets should be able to exert a force over a distance so I wouldn't think you'd need direct contact.

I did make a very rough sketch to take a peek at the gear idea.
Image
And I think it may be theoretically possible to connect the two white areas with gears hidden in the blue pieces.

And here is a quick sketch showing the eternal bridge idea of how the inner white ring could be locked to the rest of the 6×6×6.
Image

This is just 3 ideas... I suspect there are others that could work as well.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 4:01 pm 
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yes, but the gear idea looks overly complicated, the external connections looks easy enough combined with the magnet idea to allow the parts to turn normally.
To be honest though I think the floating pieces idea would be easiest. (have the internal white ring connect to the outer 6x6 part with a v-cube style mech, and have the blue ring not actually touch the core, but be held in by the gaps between the outer 6x6 part and inner white ring.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 4:19 pm 
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elijah wrote:
yes, but the gear idea looks overly complicated,
I think so too...
elijah wrote:
the external connections looks easy enough combined with the magnet idea to allow the parts to turn normally.
You could recess the blue pieces and the external bridge wouldn't even have to protrude from the surface of the cube.
elijah wrote:
To be honest though I think the floating pieces idea would be easiest. (have the internal white ring connect to the outer 6x6 part with a v-cube style mech, and have the blue ring not actually touch the core, but be held in by the gaps between the outer 6x6 part and inner white ring.
Yes, but then you don't have a true 6×6×6+4×4×4+2×2×2 cube. You need to tie the blue pieces rotation to the 2nd layer down somehow. Maybe that could be done with magnets.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Sep 20, 2009 6:08 pm 
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mm, i see your point...
I think you'd be best off recessing the blue ring slightly to allow external connections and using small magnets so that the connection pieces could come apart during second and 4th layer turns.(magnets would not be required but would greatly increase the stability of the puzzle.

Or, if you really want to go this route, the 6x6 part until you hit the inner 2x2 part could be transparent and fairly thin so that you could see the underlying 4x4 ring would be visible and able to connect to the core, the blue ring would be anchored to the second or 4th layer and the inner white ring would connect right where you would expect it between the blue and red ring, but the transparent plastic surfaces would force it to move with the rest of the 1st layer.
Unfortunately, transparent plastic resin does not work very well in any way.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Wed Sep 23, 2009 8:47 pm 
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wwwmwww wrote:
elijah wrote:
Even with magnets, you'd still need surfaces touching and therefore the blue pieces would be floating.
Well the magnets should be able to exert a force over a distance so I wouldn't think you'd need direct contact.

I did make a very rough sketch to take a peek at the gear idea.
Image

That looks like it would be extremely easy to break. The tolerance of the parts in the puzzle would have to be practically zero, seeing the current method of using screws/springs/rivots to keep puzzles together (Rubik's 4x4x4 is the only cubic design I can think of that uses no springs). Also, unless the gears are made out of stainless steel, expect them to grind together and wear down. Then you have misaligned rows and all sorts of other abnormalities. Magnets are simply not strong enough to keep the parts together. Neodymium perhaps, but not with a thick wafer separating them.

[quote=wwwmwww]I've asked about this nomenclature twice before, here and here.[/quote]I feel so privileged that you linked to my old thread:http://twistypuzzles.com/forum/viewtopic.php?p=125175 One aspect that was discussed was that the single pair of swapped tredges on a 5x5x5 are only swappable when and only when there is an odd parity of turns on the [virtual internal] 3x3x3 mech. And the algorithm for solving that parity, which I don't have handy atm, left the internal 3x3x3 entirely intact save for a single 90 turn on the R face. Parity works :idea:

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Thu Sep 24, 2009 7:04 am 
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stardust4ever wrote:
That looks like it would be extremely easy to break. The tolerance of the parts in the puzzle would have to be practically zero, seeing the current method of using screws/springs/rivots to keep puzzles together (Rubik's 4x4x4 is the only cubic design I can think of that uses no springs). Also, unless the gears are made out of stainless steel, expect them to grind together and wear down. Then you have misaligned rows and all sorts of other abnormalities. Magnets are simply not strong enough to keep the parts together. Neodymium perhaps, but not with a thick wafer separating them.


Agreed... if the gear method were used to lock the two white areas together the gears would have to be made out of stainless steel. If fact the whole thing would probably have to be made out of stainless steel and be a foot across to have a chance of working. Far from ideal... but in theory I think it could work. In practice... we've got a long way to go.

As far as magnets... I mention there use not for holding the puzzle together but solely for linking movement in one of two cases.

(1) You could build a core for a 6x6x6 that functioned as a 2x2x2. That takes care of the red area. Next the 6x6x6 could be built using the V-cube mech as normal. Then groves could be cut that would hold the blue area and allow it to turn. The problem with this method is I see no way to link the movement of the second layer to the blue area. So if magnets could be used for this they wouldn't be in contact so maybe Neodymium with some of the white 6x6x6 internals seperating them would work.

(2) You could build a 2x2x2 core as before. On top of this build a 4x4x4, so now the blue area is linked to the core. You could now build most of the 6x6x6 on top of the 4x4x4. I just don't see a way to link the face centers of the 6x6x6 to the rest of the 6x6x6. Again the white ring would be floating in a grove cut in the 4x4x4 and 2x2x2 that would hold it in place. And mabe Neodymium could be used to link its movement with the rest of the 6x6x6 with some of the 4x4x4 internals providing the needed seperation.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Thu Sep 24, 2009 7:51 pm 
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but, with such a method, 7x7 would be your absolutely maximum point, because for say, an 8x8 you would have 2 rings floating and magnets I doubt would work to keep 2 rings connected to the core but seperate from eachother.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Fri Sep 25, 2009 8:02 am 
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elijah wrote:
but, with such a method, 7x7 would be your absolutely maximum point, because for say, an 8x8 you would have 2 rings floating and magnets I doubt would work to keep 2 rings connected to the core but seperate from eachother.


For the 8x8x8 Multicube you might actually need more then 2 floating rings. You'd need one for the 6x6x6 face centers as before. You'd one for the 8x8x8 face centers. And I think you might need another one for the 8x8x8 as I'm not sure all the rest of it could be represented as the outer most layer. I'm not sure I haven't thought that far ahead. I think it will be a while before we ever see someone attempt the 6x6x6 Multicube and it's got plenty of its own challenges. But I would stop short of saying the 8x8x8 Multicube is impossible. Aside from magnets, gears could be used, and there is also the idea of external bridges (also discussed above). These 3 ideas all used in the same puzzle I think could make an 8x8x8 Multicube possible in theory. I don't think anyone would ever be crazy enough to try and build it that way though. I suspect there may be some other ideas that I haven't thought of yet that may make these types of puzzles easier. I hope so. I suspect we'll see the 5x5x5 Multicube within the next year or two. I'd LOVE to see the 6x6x6 Multicube in my lifetime. Beyond that... we may be just talking theory. There is always the CubixPlayer2 program so we aren't totally empty handed.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Fri Sep 25, 2009 5:01 pm 
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wwwmwww wrote:
I suspect we'll see the 5x5x5 Multicube within the next year or two. I'd LOVE to see the 6x6x6 Multicube in my lifetime. Beyond that... we may be just talking theory.


Don't be silly, I bet the 5x5 multicube will happen this year or early 2010. And I think the external bridge idea would work best for the 6x6 multicube. You could cast pieces like that in fact, which would make it actually feasable to be made by individuals. Anything higher than that though would be tough.

Dude, to be honest, I'd be depressed if most of what we're talking about in the forum now wasn't made before I or you dies.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Sep 26, 2009 7:52 pm 
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In the subject of this thread I called these [s]Super[/s] Super Cubes or MultiCubes a subgroup of the Circle Cubes. Well it now appears it may be more accurate to think of that as the other way around. See this post. Interesting...

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Sep 28, 2009 8:00 pm 
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wwwmwww wrote:
In the subject of this thread I called these [s]Super[/s] Super Cubes or MultiCubes a subgroup of the Circle Cubes. Well it now appears it may be more accurate to think of that as the other way around. See this post. Interesting...
Ok... looks like I jumped the gun.

I see a few problems with this explanation:

Andreas Nortmann wrote:
wwwmwww wrote:
(2) Its easy to see the Crazy 4×4×4 cube I is equivalent to a 2×2×2 inside a 4×4×4. What about II, III, and IV? Version IV looks to be a complete 2×2×2 inside a complete 4×4×4 plus some other cubies. And versions II and III don't have a complete external 4×4×4. Is there a similiar interpretation to these puzzles as with version I being one puzzle inside another? If so I can't see it.

Here is my solution:
Think of a 6x6x6 where you connect all corners with bridges to each other. Only the 12 slices (a.k.a. sides and slices of the 4x4x4) are left over. Then render these corners and all the edge pieces invisible. The inner pieces of the circles are the core pieces of the 4x4x4 made visible. The version 1,2,3,4 differ from each other which of the remaining outer pieces of the 6x6x6 are retained. For version 1 you don't need this explanation but it doesn't contradict as well.
I believe this says the outer puzzle is the face pieces of a 6x6x6 and the inner puzzle is a normal 4x4x4.

Looking at this picture:

Image

(1) Look at the green and orange pieces of the outer puzzle that are rotating in the above picture. If these were the face pieces of a 6x6x6 then none of the yellow pieces should be moving as they would be in another layer of the 6x6x6. A 4x4x4 constructed in this fashion from a 6x6x6 would be a babyface 4x4x4 and that is NOT how the outer puzzle behaves here.
(2) Same picture... now look at the top 2 green circle pieces. They are rotating... but if this is a 4x4x4 then those are the edge pieces and they should be locked to the 2 yellow circle pieces above them and they are not.

Thinking some more... the outer puzzle looks to be a 4x4x4 and the inner puzzle (inside the circles) is the face pieces of a 6x6x6. However its not a normal 6x6x6. The outer layers of the 6x6x6 only rotate with the core layers that are 2 layers below them. If the layer in the below picture is rotated then the top red face MUST be rotated with it.

Image

Here is another way to look at it. All these moves are tied together on this 6x6x6:

http://www.randelshofer.ch/cube/cube6/?MRR
http://www.randelshofer.ch/cube/cube6/?MUU
http://www.randelshofer.ch/cube/cube6/?MFF
http://www.randelshofer.ch/cube/cube6/?MLL
http://www.randelshofer.ch/cube/cube6/?MDD
http://www.randelshofer.ch/cube/cube6/?MBB

If I'm right this puzzle isn't really a subeset of a Type 1 6x6x6 Multicube after all... well maybe some weirdly bandaged Type 1 6x6x6 Multicube. Assume the 6x6x6 in the first post is a functional Type 1 6x6x6 Multicube where the blue pieces are tied to the rotaion of the layer below the top one and the red pieces are tied to the core layer rotation below that one. Now bandage that puzzle like this:

Image

Now the white pieces are tied to the red pieces and all of the Crazy 4x4x4 Cubes (Types I, II, III, and IV) are a subset of this puzzle. The blue pieces become of the outer 4x4x4 and the pieces of the white 6x6x6 are what is seen inside the circle on the faces of the Crazy 4x4x4 Cubes. The difference between the 4 types is then what pieces of the 6x6x6 and the 4x4x4 are seen. None of them show the edges of the 6x6x6 puzzle this one has however.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Sep 28, 2009 8:47 pm 
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I think you're overthinking things.
Literally, the crazy 4x4s are a 2x2 inside a 4x4, part of a 4x4 inside a 4x4 or a full 4x4 inside a 4x4.
This does behave like a bandaged multi-6x6, but in the end it is just a 4x4 inside a 4x4, much like a 3x3 could be seen as a bandaged 5x5 and such with many puzzles.
We shouldn't really worry about what they technically are though so much as how to build them. I'm positive you could make a 6x6 multicube if you ommitted the 6x6 face centers... this would also be a pretty interesting puzzle.

P.S. I think it's funny how for the most part this is a discussion between me and you rather than a discussion between people who have actually worked with innovative ideas like this.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Sep 28, 2009 9:15 pm 
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Tis not a 4x4 inside a 4x4. I'm really too tired to explain.

Just trust me.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Sep 28, 2009 9:15 pm 
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elijah wrote:
I think you're overthinking things.
Literally, the crazy 4x4s are a 2x2 inside a 4x4, part of a 4x4 inside a 4x4 or a full 4x4 inside a 4x4.
Yes, type I is a 2x2x2 inside a 4x4x4. But types II, III, and IV do NOT have a 4x4x4 inside. The edges of the supposed 4x4x4 are not connected from one face to the other. What you are looking at is a babyface 4x4x4 which ARE the face pieces of a 6x6x6 and that 6x6x6 is bandaged as I described above. And due to that bandaging the 6x6x6 face centers mirror the 2x2x2 on the inside so this description is general and applies to type I as well.

elijah wrote:
This does behave like a bandaged multi-6x6, but in the end it is just a 4x4 inside a 4x4, much like a 3x3 could be seen as a bandaged 5x5 and such with many puzzles.
Only problem is... its NOT a 4x4x4 inside a 4x4x4. Figuring out what it is... is half the fun. To me at least....

elijah wrote:
We shouldn't really worry about what they technically are though so much as how to build them. I'm positive you could make a 6x6 multicube if you ommitted the 6x6 face centers... this would also be a pretty interesting puzzle.
You have to understand what you are building before you can build it. Can't let the cart get too far ahead of the horse. And yes... a 6x6x6 Multicube minus the 6x6x6 face centers would indeed be an interesting puzzle. One with the face centers... I'd find MORE interesting. ;)

elijah wrote:
P.S. I think it's funny how for the most part this is a discussion between me and you rather than a discussion between people who have actually worked with innovative ideas like this.
I like to think I work with innovative ideas. Have you seen this thread?
http://twistypuzzles.com/forum/viewtopic.php?f=1&t=6187

Granted I don't have deep pockets or experience making resin molds but I enjoy thinking about these topics and I'm more then happy to share my ideas here. If ANYONE wants to put ANY of these ideas to practice I ask nothing in return. Personally I'm a math/theory geek and I get almost as much fun from trying to understand these puzzles (how could they be made, modeled, solved, ect.) as I would get playing with a physical one. Note I said almost. And its certainly a lot cheaper.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Sep 28, 2009 11:37 pm 
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yes, I have seen that thread, which is what I was almost reffering to with the transparentcy idea of mine above to create the 6x6 multicube.
To be honest though, I'm not sure I understand that wearing the mech on the outside idea or how it works... at all.
Also I think I'm understanding what your saying about the 6x6 centers...
Are you saying it's kinda like a cut down 4x4 cross cube, with centers glued to the core?
If not, then your gonna have to explain it in more simplistic terms or with diagrams... or both.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Tue Sep 29, 2009 11:23 am 
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elijah wrote:
yes, I have seen that thread, which is what I was almost reffering to with the transparentcy idea of mine above to create the 6x6 multicube.
To be honest though, I'm not sure I understand that wearing the mech on the outside idea or how it works... at all.
It's basically a 3x3x3 inside a 5x5x5. Think of the mech for the 3x3x3 as being on the outside of the 3x3x3, its still within the 5x5x5. It's an idea that should work in theory... in practice I'm sure it has several problems. I think the circle cube idea is something that might be used to make these Multicubes a reality before the mech on the outside idea does.

Anyways... that idea came to me after seeing this.
http://www.youtube.com/watch?v=CNk-M1Vo7f4
The first mech on the outside cube.... a bit on the large size.

elijah wrote:
Also I think I'm understanding what your saying about the 6x6 centers...
Are you saying it's kinda like a cut down 4x4 cross cube, with centers glued to the core?
Yes... I believe a 4x4x4 cross cube is the same thing as a 4x4x4 babyface cube where the face pieces have been given some thickness and the sides colored. So cut it down so you don't see those colors and you have a 4x4x4 babyface cube.... aka your cut down 4x4x4 cross cube. All in all its just another way of saying the face pieces of a 6x6x6.

elijah wrote:
If not, then your gonna have to explain it in more simplistic terms or with diagrams... or both.
No, I think you've got it.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Oct 03, 2009 10:42 am 
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wwwmwww wrote:
Now the white pieces are tied to the red pieces and all of the Crazy 4x4x4 Cubes (Types I, II, III, and IV) are a subset of this puzzle. The blue pieces become of the outer 4x4x4 and the pieces of the white 6x6x6 are what is seen inside the circle on the faces of the Crazy 4x4x4 Cubes. The difference between the 4 types is then what pieces of the 6x6x6 and the 4x4x4 are seen. None of them show the edges of the 6x6x6 puzzle this one has however.
Arg... Double Arg... looks like I need to correct my correction above.

The bandaging I discuss above (the black lines) is equivalent to all these bridges. And notice all the edges and corners of the 6×6×6 are locked to the face pieces. That means the Crazy 4×4×4 Cube Type III does in effect have the edges and corners of the 6×6×6. If you've solved the circles on the Crazy 4×4×4 Cube Type III you know you've solved the full 6×6×6 even though the edges and corners aren't seen.

Image

This also means there is some actual bandaging/bridging on the Crazy 4×4×4 cubes too... as seen above.

So... I had to ask myself... if those extra cubies don't add anything to the puzzle... why add them? Maybe elijah was right... Maybe I and EMarx were wrong.

elijah wrote:
I think you're overthinking things.
Literally, the crazy 4x4s are a 2x2 inside a 4x4, part of a 4x4 inside a 4x4 or a full 4x4 inside a 4x4.

EMarx wrote:
Tis not a 4x4 inside a 4x4.
And it appears ;) elijah has accused me of not being willing to actually get my hands dirty.

elijah wrote:
P.S. I think it's funny how for the most part this is a discussion between me and you rather than a discussion between people who have actually worked with innovative ideas like this.
So... no more crude sketches in paint. Time to roll up my sleeves and get out my trusty X-Acto knife I just got from Sufficiently Advanced Technologies, Inc.

First... I select one of my trusty spare 4×4×4 that I have around the house.

Image

With my trusty X-Acto knife I peel away the cubies being careful not to disturb the stickers. Now without those plastic cubies bandaging stickers together at the corners and edges I have a great Babyface 4×4×4. Rotation on the puzzle is excellent! ;)

Image

In fact, without that pesky friction caused by plastic on plastic contact... turning is nearly perfect.

So... now that I have a Babyface 4×4×4 what can I do with it? I got an idea... lets see if I can bandage it up to make a normal 4×4×4. Now using some bridges I ordered from Shapeways in Black Glaze and Blue Glaze I've made this glueing them to the stickers.

Image

Now I just need 21 more blue bridges to finish off the other edges and 21 more black bridges to finish off the other corners... and I have a normal 4×4×4. Cool!!! But let me save that money as I think I'm going to need it for my next idea.

Is that the only way to bandage/bridge up a Babyface 4×4×4 into a normal 4×4×4... or at least a puzzle equivalent to a normal 4×4×4? No... *evil grin*... now here is where I had to blow the budget and buy some bridges from Shapeways in Black Glaze Vibratium and Blue Glaze Vibratium. The dye they used to color the Vibratium was perfect. It slowed down the vibration in the Vibratium just enough to make it corporeal enough to glue to the stickers yet they are non-corpreal enough that they can pass through each other with just a small amount of friction. Again I only bought 3 of each and you really don't want to know what that set me back... but its enough for a proof of concept. See below...

Image

Now just do the above to the other corners and you have what I'll call an Inside Out 4×4×4. Again the black bridging defines the corners, the blue bridging defines the edges, and the stickers without bridges (on the 2×2×2 nearest you) are the face centers of a 4×4×4. It looks a bit different then your typical 4×4×4 but it behaves exactly the same and solves exactly the same way. Notice the following using the notation here applied to the above images (orange=front, yellow=up, and green=right):

On the 4×4×4 the move MR turns the yellow/orange edge and the yellow and orange face centers next to that edge.
On the Inside Out 4×4×4 the move R turns the yellow/orange edge and the yellow and orange face centers next to that edge.

On the 4×4×4 the move R turns the yellow/orange/green corner and the yellow/green and orange/green edges next to that corner.
On the Inside Out 4×4×4 the move MR turns the yellow/orange/green corner and the yellow/green and orange/green edges next to that corner.

And the same relationship holds for all the other turns. So an Inside Out 4×4×4 maps perfectly to a 4×4×4 using this:

R --> MR
MR --> R
U --> MU
MU --> U
F --> MF
MF --> F
L --> ML
ML --> L
D --> MD
MD --> D
B --> MB
MB --> B

And you can even used the same table to map a 4×4×4 to an Inside Out 4×4×4. So let's add to that notation and say MMR = R. Or if I had a sequence of moved that solve a 4×4×4 then the set of turns M(sequence) will solve the Inside Out 4×4×4 assuming its corners, edges, and face centers start from the same state. Keep in mind these cubies aren't in the same position as they are on a typical 4×4×4.

Why would anyone do this? Well Daqing Bao has already done it and more. He's hidden an Inside Out 4×4×4 inside a typical 4×4×4 with his Crazy 4×4×4 puzzles. Which... if I'm finally correct this time... means I think I've found a way to solve them. Just follow these steps:

    1. Map the circle pieces (which is an Inside Out 4×4×4) to a normal 4×4×4.
    2. Solve that normal 4×4×4 as you normally would. You now have a Crazy 4×4×4 with the circle areas solved.
    3. Solve the outer 4×4×4 of the Crazy 4×4×4 without mixing up the circle areas. This can be done by finding a sequence (called S) where S solves a normal 4×4×4 but the sequence M(S) does nothing to a 4×4×4.

Ok... so maybe I haven't actually solved a Crazy 4×4×4... but I *think* I've proven that its equivalent to finding a sequence S with the above property.

Personally my gut is having a hard time seeing how a sequence S can drastically change a 4×4×4 while at the same time the sequence M(S) does nothing to it but my brain is telling me they must exist.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Oct 03, 2009 3:07 pm 
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I think that makes sense....
I can't say honestly.

I don't understand how adding pieces even if the internal face center parts were 6x6 pieces wouldn't add to difficulty though.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Oct 03, 2009 8:10 pm 
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elijah wrote:
I don't understand how adding pieces even if the internal face center parts were 6x6 pieces wouldn't add to difficulty though.


That bandaged 6x6x6 is the same puzzle as the Inside Out 4x4x4. How do those extra pieces not add to the difficulty? Well it's because they are all bandaged to pieces on the Inside Out 4x4x4. See the first picture in my last post above. Another way to think about it... let's say I add a cubbie to a 3x3x3 by glueing it to a face center. I've certainly not made the original 3x3x3 any more difficult. Let's say I unbandage that added cubbie and allow it to rotate. It would behave as a 5x5x5 face center and multiply the total number of states for the 3x3x3 by 4 assuming the sides of the protruding cubbie were stickered. So maybe you could say that made the puzzle more difficult.... however if you could solve a 3x3x3 and couldn't solve this 3x3x3 with the rotating protruding cubie because of the added difficulty.... well that would be pretty sad.

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sat Oct 03, 2009 9:15 pm 
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That picture of yours looks like a 4x4x4 that was attacked by a set of space cubes :lol: http://www.spacecubes.com/ Another old puzzle. Mid 1990's. If you are just playing around, they might be cheaper than shapeways too. 3 sets of cubes is only US$15.

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Oct 04, 2009 2:10 am 
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wait a sec... you seriously made this?
There's no way you made a babyface 4x4 from a 4x4... :?

P.S. I thought the whole making it thing was a very subtle joke...

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Oct 04, 2009 5:10 am 
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Cool pictures!
I think this "Inside Out 4x4x4" is another valid and good way to explain how the Crazy 4x4x4 functions. I haven't thought that there are so many different ways to explain it. Well done!

For my own pride I have to state this: The Babyface 4x4x4 is a 6x6x6 without visible corners and edges. The mistake I made above dealt with the way of bandaging the virtual 6x6x6.

elijah wrote:
I don't understand how adding pieces even if the internal face center parts were 6x6 pieces wouldn't add to difficulty though.
Difficulty is highly subjective. Imagine a Nintendo Barrel with 3 or 4 layers instead of 2. It would consume more time to solve it but it wouldn't be more difficult. Number of pieces and/or number of permutations are almost useless for determining difficulty.
And as everybody can see here, recognizing the inner function of a Crazy4x4x4 is far from being trivial. Maybe this is the difficult point in these puzzles.


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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Oct 04, 2009 5:21 am 
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I ordered a Crazy 4x4 cube from MF8 one week ago :D I'm expecting them by haloween at the latest :D

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Oct 04, 2009 9:41 am 
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elijah wrote:
I don't understand how adding pieces even if the internal face center parts were 6x6 pieces wouldn't add to difficulty though.
Here is maybe an easier way to see it:

http://www.randelshofer.ch/cube/vcube6/?T3F-T3RNLNB2NRT3R-NDNLT3B2NU-NU2T3UT3RT3FNRND-NF-NB-T3L-T3F2NUNBNFND2NL2T3RND2NRT3D-NR-T3U-NLT3B-T3R2T3LT3L2T3D2T3DNL-ND2T3B-T3U2NU-NF2T3B2NU-NR2NR2T3RT3B

I've applied a random series of twists on the 6x6x6 that are allowed by the bandaging discussed above. Notice how the edges and corners don't really add anything?

Image

Carl

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Sun Oct 04, 2009 1:40 pm 
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ya... I'm pretty sure that the crazy 4x4s don't work that way...
especially if it was a cross 4x4 as you said, in which case all outer 6x6 corners and edges would be non-existent...
Plus, even if it didn't prove more difficult, that doesn't mean the inventor knows that... :wink:

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 Post subject: Re: [s]Super[/s] Super Cubes (a sub group of the Circle Cubes)
PostPosted: Mon Nov 09, 2009 10:59 pm 
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Anyone notice the Crazy Six puzzle Oskar just posted to Shapeways?

http://www.shapeways.com/model/62974/crazy_six.html

Image

Oskar... have you been reading this thread? Good for you... I hope this provided the inspiration. If not then I can say great minds think alike. :) Add a few more pieces on to this and we have the makings of the first 6×6×6 Multicube.

Keep up the great work...
Carl

P.S. I renamed the thread as I like Jared's name MultiCubes better then the name [s]Super[/s] Super Cubes.

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 Post subject: Re: MultiCubes (a sub group of the Circle Cubes)
PostPosted: Mon Nov 09, 2009 11:47 pm 
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Told you it would not only be made in your lifetime but within a few years! I told you! I told you!

But anyway, just make that puzzle allow for an internal 4x4 center area and some 4x4 pieces to the 6x6 and you have a full 6x6 multicube minus the complicated idea of the inner 6x6 centers...

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