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 Post subject: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3x3x3Posted: Mon Jan 31, 2011 11:31 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... I had a very interesting day. It started with:
GuiltyBystander wrote:
(so close you probably couldn't build this puzzle)

You tell a designer something can't be made and the first thing that pops into his head is "Ok... how can I make this puzzle?". I made my "Never say never" post and got in the shower this morning to get ready for work. While in the shower the Puzzle idea I presented above popped into my head without me even having to think about it. Let's call it the Futtminx Plus. I haven't had a moment like that since the Thorny Cube popped into my head back on Jul 09, 2010.

Seeing as Oskar already has a Futtminx design I emailed him to offer to sponsor a Futtminx Plus puzzle. He emailed me back wanting more details and asking some VERY VERY good questions. Was my idea unique to the Truncated Icosahedron geometry? Could it be applied to other geometries? If yes, how simple can that geometry be?

I just LOVE the way he thinks. He pushes you to all the right answers before you even know you had a question. He did the same thing for me with the Slice Mixup Master Skewb which I still need to finish by the way... but back to the topic at hand.

Let's see... what make's the Futtminx Plus possible. It's the fact that the 12 pentagonal faces have deeper cuts then the 20 hexagonal faces. And a combination of extra stored cuts as on the Constallation Six and fudging allows the hexagonal faces to be rotated by 60 degrees, half of the 120 degrees allowed in a normal Tuttminx.

So do I really need a puzzle with ALL these faces to get pieces like these. No!!! How simple can I make it? On the Truncated Icosahedron opposite faces are always the same so that tells me I need at least 2 of the deeper cut faces. The Truncated Icosahedron also has MORE of the shallow cut faces then the deeper cut faces so let's see if I can get away with 4 of those. The answer is yes I can. Let's look at this 3x3x3:

The orage face and its opposite are deeper cut then the other 4. And the more common shallower cut faces are limited to 180 degree turns. This is the perfect analog to the Tuttminx. So what is the process I went through to turn the Tuttminx into the Futtminx Plus? Can I use that exact same process here? And YES I can....

We need to add the stored cuts that allow the shallower cuts to be turned by 90 degrees and yet allow it to remain a doctrinaire puzzle. Cutting its normal turn of 180 in half just as the 120 degree turn on the Tuttminx is cut in half to allow the 60 degree turns.

Once you do this you have this puzzle:

Keep in mind the Orange face center cubie is twice as deep at the other cubies so the orange layer can ONLY be turned along the orange cut plane I highlight on the image on the right. So this really is a 3x3x3... NOT a 5x5x5. What makes it different from a normal 3x3x3 is the fact that one axis is NOT the same as the others. This is the anisotropic cube... expect... Oskar already coined that term for his Anisotropic Gear Cube. Is it fair to call this the Anisotropic 3x3x3?

Notice this property is also true on this puzzle:

GuiltyBystander wrote:
At each "edge position" on a face, it will always move 1 big edge + 1 thin crescent edge regardless if you are turning a pentagon or a hexagon. The difference is the order that they are in. The pentagon moves them with the big edge on the inside and crescent on the outside. The hexagons are the exact opposite with the crescents on the inside and big edges on the outside.

Except here the "big edges" are the pieces I show in blue here and the "crescent edges" are the pieces I've colored in red.

Even the equivalent of GuiltyBystander's square and long rectangle piece are present on this puzzle.
GuiltyBystander wrote:
Anyways... Interesting new pieces. Every time I see these fractal pattern of pieces, I'm completely baffled on how to solve them. I'm not talking about just those tiny dusty pieces. I don't even see an immediate solution for the square and long rectangle ones.

The "long rectangle" pieces are now colored blue and the "square" pieces are red.

So has this Anisotropic 3x3x3 been built before? How hard would it be to modify a 5x5x5 to turn like this? Making a 5x5x5 look like this is trivial as you just glue all the face pieces together on two opposite faces, however remember this "big" face center cubie is TWO layers deep so you are restricted to three turnable layers per axis, the two faces and the slice layer.

So is this an original idea? Did I really discover a NEW 3x3x3?

Carl

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Last edited by wwwmwww on Fri Jun 10, 2011 12:02 am, edited 8 times in total.

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 Post subject: Re: Shim's Constellation SixPosted: Tue Feb 01, 2011 1:25 am

Joined: Sun Oct 08, 2006 1:47 pm
Location: Houston/San Antonio, Texas
wwwmwww wrote:
Once you do this you have this puzzle:

Keep in mind the Orange face center cubie is twice as deep at the other cubies so the orange layer can ONLY be turned along the orange cut plane I highlight on the image on the right. So this really is a 3x3x3... NOT a 5x5x5. What makes it different from a normal 3x3x3 is the fact that one axis is NOT the same as the others. This is the anisotropic cube... except( )... Oskar already coined that term for his Anisotropic Gear Cube. Is it fair to call this the Anisotropic 3x3x3?

I LIKE IT!!!!!!!!

wwwmwww wrote:
So has this Anisotropic 3x3x3 been built before?

No, I don't believe it has
wwwmwww wrote:
How hard would it be to modify a 5x5x5 to turn like this?

Actually, incredible difficult I think.... The problem is the current 5x5x5 design (they're all the same in this regard so we might as well just call it a single design) is actually a 3x3x3 design with an extra layer suspended between the pieces that are actually locked into the core. This means that the 2nd layer down from all sides is incredibly difficult to control from the internals. These pieces simply slide around in a ring. Although you can stop them by bandaging some external pieces together, I can't see any practical way of forcing them to move with the outer layer for your deeper cut rotations without bandaging something, blocking other movements.
The good news is I am pretty sure a mech is possible, (even more reasonably so than most of your other ideas! ) but I think you're going to have to start from scratch. You need a mech that "is a 5x5x5 at the core". This statement is more of an abstract connection I have made in my mind, not an implied design. I THINK the only way to accomplish this is to start with a design that includes all 10 types of pieces (including the 3x3x3 pieces within the 5x5x5!). This will probably involve initially designing a center piece on top of another center piece, so that each may freely rotate and then bandaging the design together so that only the proper depths can rotate (2 pairs of centers will be bandaged together, the inner center of the other 4 pairs will be bandaged to the core). I'm sure it's possible to design your idea right off the bat, but I KNOW if you first design a 5x5x5 that physically houses some sort of internal 3x3x3 pieces, even if they are not visible on the surface, you will be able to bandage it into your AWESOME invention. [and thinking about it those internal 3x3x3 pieces should look FUNKY!!!! Not that it really matters as they're all going to bandaged to the centers in some form or another anyway]
wwwmwww wrote:
So is this an original idea? Did I really discover a NEW 3x3x3?

I certainly believe so , and if it hasn't been clear enough already, this is the COOLEST idea I've seen since jumbling first came about. I am so excited about it I want to write a simulator for it right away (it wouldn't be too difficult actually, I already have a majority of the code from a previous project), but alas I have a ton of homework this week and have already used up enough time today to ensure I won't be sleeping tonight. Assuming no one else writes a simulator before this weekend, I'll try to get one up and running for you then

I was honestly getting a little lost in this thread (I think to really see what you guys were talking about, I will have to read much more closely than I have) but I definitely see how this new idea came out of it! Interestingly enough, it seems that this idea generated from an error that produced an unexpected pattern This is great stuff Carl, although I suggest you start a new thread if you want people to start talking about it. Poor Timur's puzzle has been swallowed up by this neverending barrage of renderings of what the puzzle COULD have done... I'm starting to forget what the original idea looked like

I definitely think you should pursue this idea! It's definitely a keeper

Good Luck!
Matt Galla

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 Post subject: Re: Shim's Constellation SixPosted: Tue Feb 01, 2011 1:51 am

Joined: Wed May 13, 2009 4:58 pm
Location: Vancouver, Washington
wwwmwww wrote:
With the foreknowledge of your hint, I immediately saw where you were going with this picture. As I read on, I wondered "Is it going to have ALL those extra pieces? The squares? The rectangles? The crescents?" And your pictures brilliantly answer "yes, yes, yes, yes!"
Have you thought at all at what would happen if you made every axis have a different depth? It'd end up looking like a 7x7x7. It'd be like a higher order version right?

wwwmwww wrote:
So is this an original idea? Did I really discover a NEW 3x3x3?
Actually, I believe this may be an older brother of an existing puzzle. We'll start by looking at what a Circle 3x3x3 looks like on a 5x5x5. One turn on the Circle 3x3x3 corresponds to turning just the outer layer of the 5x5x5. Here's a picture showing the correspondence between the pieces. (Sorry I forgot to draw the circles on the red/blue faces)
Attachment:

circle-555.png [ 97.45 KiB | Viewed 6005 times ]
Now you'll see that if you turn just 1 layer of the 5x5x5, the internal circle pieces stay where they are. If you turn 2 layers of the 5x5x5, the circle pieces move with it. I hope you can see where this is going. With a reference chart, you'll see you have created the Venus Crazy 3x3 Plus Cube.

Now I said big brother earlier because your cube has a few pieces that the Crazy Plus Cubes do not have. I don't immediately see any equivalence to other pieces or any hidden bandaging like the circle edge pieces are "bandaged" to the centers on the Circle Cube. Can anyone else work out what these are?
Attachment:

unknown.png [ 12.91 KiB | Viewed 6005 times ]

This raises the questions: Does this mean that the Constellation 6 is some kind of funny Crazy Circle Plus Triangular Prism or are its extra bits and pieces based on a different kind of of jumbling? I'm heavily leaning towards the latter because I can't see any resemblance. Of course, it's pretty hard to see the circle cube in Carl's 3x3 too.

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 Post subject: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3x3x3Posted: Tue Feb 01, 2011 10:33 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... I figured this/these puzzles needed their own thread.

This puzzle was hinted at here. And first described in detail here.

Read those posts to come up to speed. The Uniaxial 3x3x3 looks like this:

But the orange face can only turn on the orange cut plane as highlighted on the right. This is a 3x3x3 as each axis of rotation is only cut by two cut planes and along each axis of rotation there are two face layers and a slice layer. I've changed the name from Anisotropic 3x3x3 as I felt that was too close to Oskar's Anisotropic Cube. I've now called it the Uniaxial 3x3x3. This terminology is used to describe crystals in which the index of refaction along one axis is different from the index of refaction along the other two.

http://en.wikipedia.org/wiki/Index_ellipsoid#Uniaxial_indicatrix

I figured this fit as the Uniaxial 3x3x3 has a bigger brother called the Biaxial 3x3x3. In biaxial crystals the index of refaction is distinct along all three axes. And I'll have some pics of that soon.

To keep my posts from being too big I'll break this post up into a couple.
Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 01, 2011 11:11 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Allagem wrote:
:shock: I LIKE IT!!!!!!!!
Allagem wrote:
Actually, incredible difficult I think.... The problem is the current 5x5x5 design (they're all the same in this regard so we might as well just call it a single design) is actually a 3x3x3 design with an extra layer suspended between the pieces that are actually locked into the core. This means that the 2nd layer down from all sides is incredibly difficult to control from the internals. These pieces simply slide around in a ring. Although you can stop them by bandaging some external pieces together, I can't see any practical way of forcing them to move with the outer layer for your deeper cut rotations without bandaging something, blocking other movements.
The good news is I am pretty sure a mech is possible,
Yes, and I'm pretty sure I know of atleast one. It works on paper but I'm not sure its the BEST mech. More of that in a few posts.
Allagem wrote:
(even more reasonably so than most of your other ideas! )
Yes, I do have a habit of coming up with near impossible puzzles to make. Most of the easy stuff has already been made... at least that is the excuse I tell myself at night... not that I really think its true.
Allagem wrote:
but I think you're going to have to start from scratch. You need a mech that "is a 5x5x5 at the core". This statement is more of an abstract connection I have made in my mind, not an implied design.
Ok... I'll get into it now. You familiar with my first POV-Ray design? It was a 5x5x5 but I called it a 3x3x3. I made this back in 1997. Fill this with 27 cubies and then start gluing cubies together. You could make the core of this puzzle a 1x1x3 that held all the other cubies. I'm not sure this is the best way... but it is A way. Still working on coming up with something better. Oskar has a concern about how I could prevent people from trying to make the apparent 5x5x5 like turns that aren't allowed. Apparently that is why the second version of the Gear Cube had its gears on the outside. Two ideas to address that... One, you could put a number on each face center stating how many cubies deep that layer was. Two you could put a square recess almost 2 cubies deep in the center of the big face centers. That would show that cubie was present in both of the apparent outer layers.

I'm open to other ideas on either how to best make this puzzle or even on how best to make it obvious where the rotation planes are located. The Biaxial 3x3x3 takes both of these issues and makes them MUCH bigger but let's not get the cart before the horse.
Allagem wrote:
(I THINK the only way to accomplish this is to start with a design that includes all 10 types of pieces (including the 3x3x3 pieces within the 5x5x5!). This will probably involve initially designing a center piece on top of another center piece, so that each may freely rotate and then bandaging the design together so that only the proper depths can rotate (2 pairs of centers will be bandaged together, the inner center of the other 4 pairs will be bandaged to the core). I'm sure it's possible to design your idea right off the bat, but I KNOW if you first design a 5x5x5 that physically houses some sort of internal 3x3x3 pieces, even if they are not visible on the surface, you will be able to bandage it into your AWESOME invention. [and thinking about it those internal 3x3x3 pieces should look FUNKY!!!!
Not necessarily... In my design above all the mech was in the outer cubies. The inner 27 could be all identical plan jane cubes.
Allagem wrote:
I certainly believe so , and if it hasn't been clear enough already, this is the COOLEST idea I've seen since jumbling first came about. I am so excited about it I want to write a simulator for it right away (it wouldn't be too difficult actually, I already have a majority of the code from a previous project), but alas I have a ton of homework this week and have already used up enough time today to ensure I won't be sleeping tonight. Assuming no one else writes a simulator before this weekend, I'll try to get one up and running for you then
Thanks for the kind words and I look forward to seeing your simulator.
Allagem wrote:
I was honestly getting a little lost in this thread (I think to really see what you guys were talking about, I will have to read much more closely than I have) but I definitely see how this new idea came out of it! Interestingly enough, it seems that this idea generated from an error that produced an unexpected pattern This is great stuff Carl, although I suggest you start a new thread if you want people to start talking about it.
Done... And yes... if you see an error that's interesting (this was) why not exploit it? I owe it all to GuiltyBystander's great pictures and Oskar's great questions for pointing me in the right direction, add to that Timur's great puzzle which sparked the whole discussion.
Allagem wrote:
Poor Timur's puzzle has been swallowed up by this neverending barrage of renderings of what the puzzle COULD have done... I'm starting to forget what the original idea looked like
I agree. It's a great puzzle and I certainly didn't mean to take any attention away from it. I just love puzzles like that that appear to break the rules and then force you to re-question all the other rules you thought were solid.
Allagem wrote:
I definitely think you should pursue this idea! It's definitely a keeper
Thanks. And I will (already am).

Carl

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Last edited by wwwmwww on Wed Feb 02, 2011 11:06 am, edited 1 time in total.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 01, 2011 11:43 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
GuiltyBystander wrote:
With the foreknowledge of your hint, I immediately saw where you were going with this picture.
I was afraid someone would see where I was going without that picture. I was almost sure the hint gave it away, and it wouldn't have been hard to see which thread I had been doing most of my posting in of late.
GuiltyBystander wrote:
As I read on, I wondered "Is it going to have ALL those extra pieces? The squares? The rectangles? The crescents?" And your pictures brilliantly answer "yes, yes, yes, yes!"
Trust me I went through all those question myself and was very happy with all the answers too.
GuiltyBystander wrote:
Have you thought at all at what would happen if you made every axis have a different depth? It'd end up looking like a 7x7x7. It'd be like a higher order version right?
I have now!!! Thanks. That is the Biaxial 3x3x3. And I have some pictures of it rendering now. The process of making it doctrinaire requires a few more steps then it does on the Uniaxial 3x3x3 so it took me a bit to realize what it would actually look like. It will be a very hard puzzle to build (at least one that will work well) and I suspect a very very difficult puzzle to solve. But believe me if I get a working Uniaxial 3x3x3 the Biaxial 3x3x3 will certainly be on my radar.
GuiltyBystander wrote:
Actually, I believe this may be an older brother of an existing puzzle. We'll start by looking at what a Circle 3x3x3 looks like on a 5x5x5. One turn on the Circle 3x3x3 corresponds to turning just the outer layer of the 5x5x5. Here's a picture showing the correspondence between the pieces. (Sorry I forgot to draw the circles on the red/blue faces) Now you'll see that if you turn just 1 layer of the 5x5x5, the internal circle pieces stay where they are. If you turn 2 layers of the 5x5x5, the circle pieces move with it. I hope you can see where this is going. With a reference chart, you'll see you have created the Venus Crazy 3x3 Plus Cube.
Cool!!!! I must confess I haven't got any of the Circle Plus Cubes as I was wanting your basic Circle Cube first and I was a bit turned off that I can't get a kit that would allow me to build all the versions. So it turns out I go and design my own and don't even realize it. Too funny...
GuiltyBystander wrote:
Now I said big brother earlier because your cube has a few pieces that the Crazy Plus Cubes do not have. I don't immediately see any equivalence to other pieces or any hidden bandaging like the circle edge pieces are "bandaged" to the centers on the Circle Cube. Can anyone else work out what these are?
Andreas Nortmann may be our best bet. If he doesn't pop up here I'll be sure to point him to this thread.
GuiltyBystander wrote:
This raises the questions: Does this mean that the Constellation 6 is some kind of funny Crazy Circle Plus Triangular Prism or are its extra bits and pieces based on a different kind of of jumbling? I'm heavily leaning towards the latter because I can't see any resemblance. Of course, it's pretty hard to see the circle cube in Carl's 3x3 too.
Well neither the Uniaxial 3x3x3 nor the Constellation 6 jumble so I'm not sure what you mean by "a different kind of jumbling". The Constellation 6 is fudged and I believe we have shown there is a relationship between fudging and jumbling but there isn't any fudging in either the Uniaxial 3x3x3 or Circle Cubes.

Carl

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Last edited by wwwmwww on Wed Feb 02, 2011 11:09 am, edited 1 time in total.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 01, 2011 11:52 pm

Joined: Tue Jul 27, 2010 10:17 am
Location: Missourica
Very cool! I would like to see this applied to puzzles that are more complex than a 3x3, yet less complex than a Tuttminx.

It would be cool to see a megaminx version (would it look like a Gigaminx?)

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Past project: The Geode
Current Project: Replica RPK-74
Future Project: Possibly another master mental
Oskar wrote:
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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:09 am

Joined: Wed Jan 07, 2009 6:46 pm
Location: Evanston, IL
Really interesting idea. I just tried to design this in solidworks, but so far, I have come to the conclusion that it cannot be done using the shell-mech (intersecting spherical cuts), or the V-mech. The problem is that you have to be able to cut off the corner at two different depths, and this makes the corner detached from the rest of the puzzle.

Eric (gingervergo) and I are both trying to work it out. I'll let you know if we come up with anything.

EDIT: Scratch that. I think it might be possible using v-mech. I'll give it a try next time I have time.

-Eitan

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:24 am

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
This is making me go insane. I spent about an hour thinking it through, and now I'm not even sure any of it will work. Expect some kind of long post tomorrow.

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:51 am

Joined: Sun Mar 08, 2009 9:21 am
Location: Massachusetts, USA
Because of how this puzzle is related to the Crazy 3x3 Plus Venus, can it be built up as an extension of the Venus? I think I've come up with a way to do this, but I haven't really checked to see if it will go together in CAD.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 11:38 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
It would be cool to see a megaminx version (would it look like a Gigaminx?)

The Uniaxial Megaminx would look like this:
Attachment:

UniaxialMM.png [ 193.81 KiB | Viewed 6982 times ]

Two opposite faces would have deep cuts and big face centers. All the other faces would have shallower cuts. So yes, it would look like a bandaged Gigaminx.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:10 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
I just realized there are 3 puzzles in this family.

This shows how the Deep Uniaxial 3x3x3 is made up from its base 3x3x3.
Attachment:

CH3x3x3.png [ 25.73 KiB | Viewed 6952 times ]

But the unique axis could also be the shallow cut one. So here is the Shallow Uniaxial 3x3x3 and its base 3x3x3.
Attachment:

Uniaxial3Shallow2.png [ 42.52 KiB | Viewed 6942 times ]

I've added lines of the colors of the faces to show you where the cut planes are located. This puzzle looks JUST like a 5x5x5 from the outside.

There is only one Biaxial 3x3x3 and my last picture of it should be finished rendering by the time I get home tonight. I say there is only one, but I guess you could count its mirror image as a different puzzle. Personally I wouldn't. If you do then there is a Left Biaxial 3x3x3 and a Right Biaxial 3x3x3.

Carl

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Last edited by wwwmwww on Wed Feb 02, 2011 12:19 pm, edited 2 times in total.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:14 pm

Joined: Tue Mar 10, 2009 7:06 pm
Location: Nowhere in particular.
I found a mechanism! I'll draw it in rhino later, but for now I'll just explain it. I spent like three hours last night examining the properties of every piece on the 5x5, and couldn't find a place to block the turns. I had a six paragraph post saved to finish up today, but still couldn't find anywhere that would work. Now, I'm in the middle of biology class, and I almost facepalmed at how simple it is.

Consider a 5x5 using the exact same rail mechanism you described in the old thread you linked to above. Now, bandage the centers of two opposing faces to create the anisotropic centers. Now, let's consider the other concept that thread illustrated- the internal 3x3. Bandage the top face of said 3x3 to the top center and do the same with the bottom center. That's it. I realize this is similar to your 1x1x3 idea, but this one requires a much simpler mechanism.

EDIT: Just read your latest post. This mechanism wouldn't work for the second puzzle you described.

_________________
~Kapusta

PB: At home (In Competition)
2x2 1.xx (2.88)
3x3 11.xx (15.81)
4x4 1:18.26 (1:24.63)
5x5 (3:00.02)
6x6 4:26.05 (6:34.68)
7x7 6:38.74 (9:48.81)
OH (35.63)

Current Goals:
7x7 sub 6:30
4x4 sub 1:10

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 12:58 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
wwwmwww wrote:
GuiltyBystander wrote:
Now I said big brother earlier because your cube has a few pieces that the Crazy Plus Cubes do not have. I don't immediately see any equivalence to other pieces or any hidden bandaging like the circle edge pieces are "bandaged" to the centers on the Circle Cube. Can anyone else work out what these are?
Andreas Nortmann may be our best bet. If he doesn't pop up here I'll be sure to point him to this thread.
Thank you for trusting me that much.
Sadly I can't find what isn't there. I could not help myself but I had to classify the CrazyPlus3x3x3's as restricted 5x5x5's. An the same applies here. That is no caputulation since the Circle2x2x2 of TomZ is nothing more (?) than a modified Fused cube => a restricted 3x3x3.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 1:12 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Kapusta wrote:
Consider a 5x5 using the exact same rail mechanism you described in the old thread you linked to above. Now, bandage the centers of two opposing faces to create the anisotropic centers. Now, let's consider the other concept that thread illustrated- the internal 3x3. Bandage the top face of said 3x3 to the top center and do the same with the bottom center. That's it. I realize this is similar to your 1x1x3 idea, but this one requires a much simpler mechanism.
From the description I don't see how this is different from my idea of appling my rail mech 5x5x5 idea to the outside of a 1x1x3. I guess I'll wait and see your pictures.
Kapusta wrote:
EDIT: Just read your latest post. This mechanism wouldn't work for the second puzzle you described.
Well again if you go back to the fully functional 5x5x5 rail mech that I link to above it should (on paper) be possible to glue/fuse four of the 5x5x5 face centers to the 3x3x3 face centers below them. That fixes the deeper cuts. And the other two 3x3x3 face centers would then be fixed to the core. This would limit you to only shallow cuts in the other direction. I just have concerns about the rail mech in general. A concern that's just as important to me is how is the solver supposed to keep track of where the cut planes are? Numbers on the face centers again?

I want to see what happens when someone gives a Shallow Uniaxial 3x3x3 to a speed solver under the guise that its a scrambled 5x5x5 and see what happens.

And here is a question for you... does the Shallow Uniaxial 3x3x3 have the same number of states as a 5x5x5? If the Shallow Uniaxial 3x3x3 can reach a state where one of the illegal but apparent slice layers appears to have been turned by 90 degrees then I think the answer is yes. And if so... it'd be even funnier to pass off as a 5x5x5 to a speed solver in this state.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 1:16 pm

Joined: Fri Mar 06, 2009 9:23 pm
without spoiling the fun for the rest of you, I think the key to making this puzzle is a puzzle tony fisher made a long long time ago

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 2:00 pm

Joined: Sun May 17, 2009 1:33 pm
Location: USA, North America, Planet Earth, Solar system, Milky Way galaxy, Universe
Since an Eastsheen 5x5x5 is mainly block-based, if you extend the center piece down further, and then extend it outwards, it should create a sufficient blocking mechanism. I'll illustrate, if necessary

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 3:45 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Monopoly wrote:
Since an Eastsheen 5x5x5 is mainly block-based, if you extend the center piece down further, and then extend it outwards, it should create a sufficient blocking mechanism. I'll illustrate, if necessary
Please do. My Eastsheen 5x5x5 I think is still in storage at the moment. The only 5x5x5 I have with me is my V-Cube 5x5x5.

Thanks,
Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 5:31 pm

Joined: Sun May 17, 2009 1:33 pm
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Ok, here's a quick edit of my idea. I don't actually own an ES 5x5x5 but from pictures of the puzzle, and diagrams from the patent I'm pretty sure that it would work. Maybe, when I next go to China I'll buy a copy and try to mod it.
The diagrams show the side and top view of the center piece. Essentially the bottom part is a block 3x3x1 units wide that will block middle layer rotation

 Attachments: File comment: Diagram showing how the center-piece would be extended, to bandage the bottom two layers. anisotropic.jpg [ 43.73 KiB | Viewed 6793 times ]

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 5:33 pm

Joined: Sun Nov 23, 2008 2:18 am
wwwmwww wrote:
The Uniaxial Megaminx would look like this:
Attachment:
UniaxialMM.png

Two opposite faces would have deep cuts and big face centers. All the other faces would have shallower cuts. So yes, it would look like a bandaged Gigaminx.

I am thinking that the Megaminx, having six axes, would have a much larger multiaxial family than the cube.

Considering just the two cut depths corresponding to a gigaminx gives several possible combinations for cut depth:

1 deep/5 shallow(Illustrated above)
2 deep/4 shallow
3 deep/3 shallow
4 deep/2 shallow
5 deep/1 shallow(Megaminx counterpart to Shallow Uniaxial Cube.)

Without considering the relative positions between deep and shallow axes, though I think 3-3 might be the only one with two distinct axis arrangements.

Not to mention variations with 3, 4, 5, or 6 different cut depths if the concept does not break down.

Anyways, I cannot wait to see the Biaxial Cube.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 8:40 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Jeffery Mewtamer wrote:
Anyways, I cannot wait to see the Biaxial Cube.

Here is the animation I was working on.

It starts with the base puzzle and turns opposite faces in pairs by 90 degrees and then adds back in the needed cuts to allow rotation only along the white cut planes. They are black on the base puzzle. It took me 9 sets of turns just to seperate all the pieces so I bet this would be one painful puzzle to solve. Ingore the rendering artifacts that are popping up on the later iterations. POV-Ray isn't good at these iterative processes so I'm not sure if that was it or the low quality settings I was using. Either way I didn't want to wait a week to see what it would look like. You end up with what looks like a 7x7x7 with a pair of 3x3 face centers on the opposite deepest cut faces.

Regarding the Megaminx options... yes you could have more then 1 axis with deeper cuts and if you did you'd cut up the large face center and end up with a puzzle that looked just like a gigaminx until you tried to turn it.

However if you really want to push it... we aren't done with the cube yet. There is nothing forcing opposite faces to have the same depth cut. We have 6 faces to play with so we could have each face cut at a different depth. If you did this you'd end up with a puzzle which looked like a 13x13x13 and all the faces but the one with the deepest cut and its opposite face would look like the faces on a 13x13x13. The face which has the deepest cut and its opposite face would have a 3x3 face in its center assuming the next deepest face was a neighboring face. If the next deepest face was opposite the deepest then I think both these faces would have 5x5 face centers, since the faces don't move relative to the cuts neither face could be cut by these two cuts. So how would you like to have a 13x13x13 which was really a 3x3x3? I suspect it would be so painful to solve and even scrable that this line of thought would have lost all its fun by this point.

Carl

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Last edited by wwwmwww on Thu Feb 03, 2011 10:05 am, edited 1 time in total.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Wed Feb 02, 2011 8:47 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Jeffery Mewtamer wrote:
Without considering the relative positions between deep and shallow axes, though I think 3-3 might be the only one with two distinct axis arrangements.
I believe you are correct.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Fri Feb 04, 2011 11:27 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
wwwmwww wrote:
And here is a question for you... does the Shallow Uniaxial 3x3x3 have the same number of states as a 5x5x5?
No.
The 5x5x5 has:
2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000
23495304646909563557559799058444533335883923581298624430080000000000000
which is factor 10461394944000 compared with CrazyPlusVenus

Please note that in an effort to make the calculation easier I defined T/X-pieces of the 5x5x5 as distinguishable but orientation of F-pieces as invisible.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Fri Feb 04, 2011 12:26 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
No.
The 5x5x5 has:
2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000
23495304646909563557559799058444533335883923581298624430080000000000000
which is factor 10461394944000 compared with CrazyPlusVenus

Please note that in an effort to make the calculation easier I defined T/X-pieces of the 5x5x5 as distinguishable but orientation of F-pieces as invisible.

NICE!!!! Could you post the code for this? I need to dig back to the thread where you calculated the number of states of the Complex 3x3x3 and learn how to use the software you are using to make these calculations. I eat this stuff up.

Is the calculation above for the Shallow Uniaxial which looks just like a 5x5x5 or the Deep Uniaxial with the 2 large face centers? How do those 2 compare?

And does this mean the Shallow Uniaxial can't get in a state where one of the illegal slices appears turned by 90 degrees? Using this notation what a 5x5x5 would look like after NU. What about an apparent 180 degree turn of that slice, NU2?

Carl

P.S. Does this mean you've already calculated the number of states of all the CrazyPlus cubes? That would be interesting to see as well.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Sat Feb 05, 2011 5:07 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Your ShallowUniaxial3x3x3 has the same number of permutations as the 5x5x5 under the conditions mentioned above.
The DeepUniaxial contains NU2 but not NU

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Sun Feb 06, 2011 3:33 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
Your ShallowUniaxial3x3x3 has the same number of permutations as the 5x5x5 under the conditions mentioned above.
NICE!!! Followed by a long evil laugh. This is exactly what I had hopped for.
Andreas Nortmann wrote:
The DeepUniaxial contains NU2 but not NU
Ok... time to go dig up the thread on the number of permutations of the complex 3x3x3 and get the name of the software you are using again. The code looks easy enough to follow. I really want to learn how to use this software. So aside from getting the number of permutations how do you tell the DeepUniaxial contains NU2 but not NU. Just how flexable is this software? And here are a few other questions if you are enjoying this as much as me:

(1) If you took a 5x5x5 apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I know you can't rotate a single corner so that knocks it down to 1 in 3. You also can't flip a single middle edge so that drops it further to 1 in 6. Am I forgeting anything?

(2) Now if you took the DeepUniaxial apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I'm guessing much less then the 5x5x5. The corner rotation and edge flip are the same, but we now know NU isn't allowed either. I'm curious if we can name all the conditions like this and see how they total up to the final odds. Or are there some very odd states that wouldn't be allowed and would be hard to describe in simple terms. Something like this:

corner twist (1 in 3)
edge flip (1 in 2)
disallow NU (1 in ?)
other (1 in A)
etc.
Total is 1 in 3*2*?*A*etc

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Mon Feb 07, 2011 12:25 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
wwwmwww wrote:
So aside from getting the number of permutations how do you tell the DeepUniaxial contains NU2 but not NU.
The programm is called GAP:
http://en.wikipedia.org/wiki/GAP_comput ... bra_system
and the code is:
Code:
wwwmwww wrote:
(1) If you took a 5x5x5 apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I know you can't rotate a single corner so that knocks it down to 1 in 3. You also can't flip a single middle edge so that drops it further to 1 in 6. Am I forgeting anything?
In this case Jaap's page is a help.

wwwmwww wrote:
(2) Now if you took the DeepUniaxial apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I'm guessing much less then the 5x5x5. The corner rotation and edge flip are the same, but we now know NU isn't allowed either. I'm curious if we can name all the conditions like this and see how they total up to the final odds. Or are there some very odd states that wouldn't be allowed and would be hard to describe in simple terms.
I can't answer this question for general puzzles under GAP yet. Sorry.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Mon Feb 07, 2011 3:18 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
The programm is called GAP:
http://en.wikipedia.org/wiki/GAP_comput ... bra_system
and the code is:
Code:

I looked it up last night and installed on on my home PC. Still not sure how to use it. The first thing I tried was to walk it through this example.
http://www.gap-system.org/Doc/Examples/rubik.html
And I'm not sure how to get it to even load the input file here.

I must confess that even if I could get that example to run I really only understand about half of it. But I did see where it shows how to tell if a state is an allowed state. For example:

gap> (1,7,22) in cube1;
false

Means you can't twist a single corner.

I think I need this [1,3,17,14,8,38,9,41,19,48,22,6,30,33,43,11,46,40,24,27,25,35,16,32].

To map 1 to 1, 7 to 9, and 22 to 35 to figure out which corner its talking about and I don't really see how that maping is being made but oh well. I think I could do:

gap> (1,9,35) in cube;

and get the same result... correct?

I even tried to copy and past this:

gap> cube := Group(
> ( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19),
> ( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35),
> (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11),
> (25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24),
> (33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27),
> (41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40) );
<permutation group with 6 generators>

into gap using Ctrl-V just to get it in there and it won't even let me past. Surely there is an easier way to get stuff like this in there without having to type it all on the command line each time you want to use it. And I'm sure its really simple too... I just haven't figured it out yet.

Andreas Nortmann wrote:
In this case Jaap's page is a help.

Thanks...
http://www.jaapsch.net/puzzles/cube5.htm

Andreas Nortmann wrote:
wwwmwww wrote:
(2) Now if you took the DeepUniaxial apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I'm guessing much less then the 5x5x5. The corner rotation and edge flip are the same, but we now know NU isn't allowed either. I'm curious if we can name all the conditions like this and see how they total up to the final odds. Or are there some very odd states that wouldn't be allowed and would be hard to describe in simple terms.
I can't answer this question for general puzzles under GAP yet. Sorry.

The total odds shouldn't be too hard to figure out... shouldn't it just be the ratio of the number permutations to the number of ways to assemble the puzzle? Breaking this ratio down to all its factors is the hard part.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 08, 2011 12:30 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... got some of the basics with GAP figured out. I started a GAP thread here.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 08, 2011 3:46 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
wwwmwww wrote:
(1) If you took a 5x5x5 apart and reassembled it randomly, what are the odds that state is reachable from the solved state? I know you can't rotate a single corner so that knocks it down to 1 in 3. You also can't flip a single middle edge so that drops it further to 1 in 6. Am I forgeting anything?
As you pointed out, the corner twist is a factor of (3). A middle edge flip is (2). The parity of the middle edges is tied to the corners so if you assemble the corners into an odd perm the middle edges need to be odd too. Or vice-versa. This is a factor of (2).

Finally, I assume you meant a theoretical 5x5x5 cube rather than a physical one. On a physical 5x5x5 you can't physically flip a edge-wing piece. If we are talking about randomly assembling a theoretical 5x5x5 cube with no physical restrictions then the orientation parity of the 12 pairs of indistinguishable edge-wing pieces must match for factor of ((2)^12).

So that would be 1 in (3)*(2)*(2)*((2)^12). Or 1 in 49152.

Hopefully I did this analysis right. I always mess these things up when I'm imagining the puzzle rather than holding/manipulating it.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 08, 2011 11:40 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
After an night I have found a simple way to calculate the quotient between the "Reassembling5x5x5" and the "TwistsOnly5x5x5":
Just add some new generators to the definition of the Group:
Code:
IllegalGenerators[13]:=(21,30,57);#Twist of a single Corner
IllegalGenerators[14]:=(23,53);#Twist of a single edge
IllegalGenerators[n]:=...;#All other parity restrictions
Very crude, but you should get the point.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Tue Feb 08, 2011 7:04 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
bmenrigh and Andreas,

Thanks for the input. I've answered/commented on you last posts but I put my reply here.

http://twistypuzzles.com/forum/viewtopic.php?p=247477#p247477

I figured it best to keep the general GAP stuff in the GAP thread over in the General Puzzle Topics area. I'll try to keep this one focused on the Axial 3x3x3's. There is some stuff I want to do in GAP just for these puzzles but while I'm learning GAP and playing with simplier questions I'll try to post over there as well.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Thu Feb 10, 2011 11:01 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
wwwmwww wrote:
Andreas Nortmann wrote:
Your ShallowUniaxial3x3x3 has the same number of permutations as the 5x5x5 under the conditions mentioned above.
NICE!!! Followed by a long evil laugh. This is exactly what I had hopped for.

Dig a little deeper and things are even more interesting...
Andreas has presented these numbers above. But here are the number of permutations for each of these puzzles:

Normal 5x5x5:
2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000

Normal Shallow Uniaxial 3x3x3:
2582636272886959379162819698174683585918088940054237132144778804568925405184000000000000000

Normal Deep Uniaxial 3x3x3:
23495304646909563557559799058444533335883923581298624430080000000000000

So it looks like the 5x5x5 and the Shallow Uniaxial have the exact same space... doesn't it? Not exactly, let's look at the Super sticker versions:

Super 5x5x5:
5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000

Super Shallow Uniaxial 3x3x3:
2644619543436246404262727370930875991980123074615538823316253495878579614908416000000000000000

Super Deep Uniaxial 3x3x3:
3007398994804424135367654279480900266993142218406223927050240000000000000

So the Super Shallow Uniaxial 3x3x3 appears to have some face center parity issue that the Super 5x5x5 doesn't have. Must dig into this further. Still getting my feet wet with GAP so this is slow going. Here is my code if anyone wants to double check me. So far its just a slightly modified version of Andreas's code posted above.

Attachment:
Super5x5x5.txt [6.94 KiB]

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Thu Feb 10, 2011 11:41 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... things just got weird.

Taking the above code I did this:

gap> (013,152,153,151) in SuperCube5;
false

This took several seconds to check but it came back false. This means you can't turn a single face center by 90 degrees on a Super 5x5x5. I think we all knew that.

gap> (013,153)(152,151) in SuperCube5;
true

GAP spit this out instantly. Must have been easy to find. So you CAN turn a single face center on a Super 5x5x5 by 180 degrees. And this is the state that I was going to guess wasn't allowed on the Super Shallow Uniaxial. So I checked.

gap> (013,153)(152,151) in SuperShallowUniaxial;
true

This also took several seconds so I was certain false was going to pop up... BUT it didn't. So now I'm at a loss, what is the other parity issue? Why does the SuperShallowUniaxial have half as many states as a Super 5x5x5?

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Fri Feb 11, 2011 12:04 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Ok... I figured it out.

gap> (088,161,162,160) in SuperShallowUniaxial;
false
gap> (088,162)(161,160) in SuperShallowUniaxial;
true
gap> (088,161,162,160)(138,167,168,166) in SuperShallowUniaxial;
false
gap> (088,161,162,160)(138,167,168,166) in SuperCube5;
true
gap> (088,161,162,160)(138,166,168,167) in SuperCube5;
true
gap> (088,161,162,160)(138,166,168,167) in SuperShallowUniaxial;
false
gap> (013,152,153,151)(138,167,168,166) in SuperShallowUniaxial;
true
gap> (088,161,162,160)(113,164,165,163) in SuperShallowUniaxial;
true

See it? On a Super5x5x5 you can rotate ANY 2 face centers by 90 degrees. However on a SuperShallowUniaxial there are two types of face centers. If you rotate a face center by 90 degrees you MUST also rotate another like face by 90 degrees too. If you rotate a face center that is 2 layers deep you must rotate one of the other three that is also 2 layers deep. If you rotate a shallow 1 layer deep face center then you must also rotate the other 1 layer deep face center, there are only two of these.

I'm really starting to like the GAP software.

Carl

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Fri Feb 11, 2011 10:29 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Nice that you could helped yourself.
You have found that parity restriction by "digging" manually?

Maybe there is a clever way to use GAP to do this for you. I don't know it either.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Fri Feb 11, 2011 10:55 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
Nice that you could helped yourself.
You have found that parity restriction by "digging" manually?

Maybe there is a clever way to use GAP to do this for you. I don't know it either.

Yes, I just tried a few things I thought it might be manually till I found it. No idea how to get GAP to do that for me. I'm still learning the basics... for example. When you combined the two outer layers into one operation I saw you used U1*U2. I haven't yet seen where * is defined so I'm taking your word for it that it does what I think it does.

Also I just realized that the numbers that I'm calling "normal" above aren't really normal, as the X-Centers and T-Centers are distinguishable and they shouldn't be on a Normal 5x5x5. What is the best way to deal with that in GAP? I don't think I could simply give all the X-Centers on a given face the same number as (007,007,007,007) I don't think would mean anything? Is there a way to define this group such that Size(Normal5x5x5) would give you the correct number?

Carl

P.S. Boy its hard to keep the general GAP stuff and the Uniaxial specific stuff in seperate theads. As these questions are general please feel free to quote this post and put your reply over in the GAP thread. Future GAP users will be much more likely to find this info there.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Sat Feb 12, 2011 6:50 am

Joined: Fri Feb 08, 2008 1:47 am
Location: near Utrecht, Netherlands
Here's a sneak peak at my shallow unaxial 3x3x3 cube. The design needs a few minor changes but generally it is quite a good puzzle.

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 Post subject: Re: The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3Posted: Sat Feb 12, 2011 4:23 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
TomZ wrote:
Here's a sneak peak at my shallow unaxial 3x3x3 cube. The design needs a few minor changes but generally it is quite a good puzzle.

NICE!!!! It looks GREAT!!! But I'm sure I'm very biased.

Carl

P.S. And that is the Deep Uniaxial. The unique axis has cuts deeper then the other two.

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 Post subject: Re: Shim's Constellation SixPosted: Mon Mar 21, 2011 5:07 pm

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
wwwmwww wrote:

Keep in mind the Orange face center cubie is twice as deep at the other cubies so the orange layer can ONLY be turned along the orange cut plane I highlight on the image on the right. So this really is a 3x3x3... NOT a 5x5x5.

This should be entirely buildable. The core is a 1x1x3, in the proportions of the center of it being a 3x3x1 block and the two ends being 3x3x2 blocks. The center faces are then held in by the core in the same way that the ends of a 3x3x5 are held in. The edges are then held in by the face centers, and the corners are held in by the edges, in much the same way that the plain old rubik's cube works and the better 4x4x4 mechanisms work.

The biggest problem in practice will be that the corners have a bit of a tendency to pop.

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 Post subject: Re: Shim's Constellation SixPosted: Mon Mar 21, 2011 8:26 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Bram wrote:
This should be entirely buildable.
It is. And it has. See TomZ's post here. Tom and I have plans to offer this on Shapeways.

I'm calling this the Deep Uniaxial 3x3x3 as the unique axis has has deeper cuts then the others. There is also a Shallow Uniaxial 3x3x3 seen in the other thread. Any tips on how best to make that one? I know one way but I have serious concerns about how stable it would be.

Carl

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