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 Post subject: Double circle cubes
PostPosted: Sun Jun 05, 2011 4:06 am 
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Hi

Can anyone tell me whether it's possible to buy any double circle cubes like the one below. And if so, where.

Thanks

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DoubleCircle.gif
DoubleCircle.gif [ 15.85 KiB | Viewed 2044 times ]

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 Post subject: Re: Double circle cubes
PostPosted: Sun Jun 05, 2011 4:13 am 
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No kind of Circle 5x5x5 exists yet, let alone a double circle one, and especially let alone a mass produced one.

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 Post subject: Re: Double circle cubes
PostPosted: Sun Jun 05, 2011 4:15 am 
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OK. Bummer. Thanks Luke.

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 Post subject: Re: Double circle cubes
PostPosted: Sun Jun 05, 2011 2:15 pm 
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Luke wrote:
No kind of Circle 5x5x5 exists yet, let alone a double circle one, and especially let alone a mass produced one.
How about a Crazy 6x6x6?
Luke wrote:
... but you don't know the difference between a 5x5x5 and a 6x6x6. I am most certainly disappointed. :lol: :lol: :lol:
When you glue the center pieces together, it becomes a Circle 5x5x5, sort of.

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Last edited by Oskar on Sun Jun 05, 2011 2:30 pm, edited 2 times in total.

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 Post subject: Re: Double circle cubes
PostPosted: Sun Jun 05, 2011 2:20 pm 
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Oskar wrote:
How about a Crazy 6x6x6?


Oskar! I am disappointed! You build puzzles which break the rules of geometry, break world records multiple times, but you don't know the difference between a 5x5x5 and a 6x6x6. I am most certainly disappointed. :lol: :lol: :lol:

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 Post subject: Re: Double circle cubes
PostPosted: Tue Jun 07, 2011 7:43 pm 
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I like your idea, but what about something more like this?

Image

It is sort of a combination of crazy 4x4x4 types 1 and 2

In my head the Theory would be when you turn the U or u layer, D stays still, F,L,B and R turn like normal. if it was U all of U but the little circle, or if it was u of of U but the big circle turns.


I like your idea alot, one day i want to see crazy stuff like
Image

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 8:55 am 
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Does the very center circle on that super crazy 9x9 even have a point?


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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 9:47 am 
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Luke wrote:
No kind of Circle 5x5x5 exists...

This one exists as POV-Ray code on my PC.

http://twistypuzzles.com/forum/viewtopic.php?f=1&t=19622

Image

Image

I need to rebuild this in Solidworks, get it printed, and see how it works... but I have several puzzles I'm working on getting into Solidworks before this one. But to my knowledge its the first fully designed circle 5x5x5.

Carl

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 10:01 am 
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damo676767 wrote:
It is sort of a combination of crazy 4x4x4 types 1 and 2

In my head the Theory would be when you turn the U or u layer, D stays still, F,L,B and R turn like normal. if it was U all of U but the little circle, or if it was u of of U but the big circle turns.


I'm not 100% sure I follow, but if I do this adds nothing to the solving challenge of a Crazy 4x4x4 Type 2. That puzzle is already equivalent to super solving a 2x2x2 inside a 4x4x4. I believe the extra pieces created by your second circle simple give you another view of pieces that are already present on the Crazy 4x4x4 Type 2. In other words if you were to solve your proposed puzzle as a Crazy 4x4x4 Type 2 you'd fine all the new pieces would be solved themselves when you were done with the Crazy 4x4x4 Type 2 pieces.

I don't think there is any value added to putting a second circle on the puzzle until you are at least to the 5x5x5.

Carl

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 10:36 am 
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damo676767 wrote:
It is sort of a combination of crazy 4x4x4 types 1 and 2

In my head the Theory would be when you turn the U or u layer, D stays still, F,L,B and R turn like normal. if it was U all of U but the little circle, or if it was u of of U but the big circle turns.

I think what you mean is it is a combination of a crazy 4x4 and a crazy 2x2. Note that in your specific example, making d turn would also turn the same circle on the top that a u turn does (as well as affecting the other-sized circle on the bottom) because of how the bandaging works for an even-layered circle puzzle (like the crazy 2x3x3). Also, I think you might have U and u switched in your description (if you had expected it to function similarly to Oskar's Crazy Six).

wwwmwww wrote:
I'm not 100% sure I follow, but if I do this adds nothing to the solving challenge of a Crazy 4x4x4 Type 2. That puzzle is already equivalent to super solving a 2x2x2 inside a 4x4x4. I believe the extra pieces created by your second circle simple give you another view of pieces that are already present on the Crazy 4x4x4 Type 2. In other words if you were to solve your proposed puzzle as a Crazy 4x4x4 Type 2 you'd fine all the new pieces would be solved themselves when you were done with the Crazy 4x4x4 Type 2 pieces.

I think the solving challenge should be completely different because on all of the "regular" crazy 4x4's, turning on the 2x2 cuts does not affect any circles, while on the double-circle 4x4 it would.

Edit: Also Carl, are the "corners" of the outer-circles missing from your puzzle intentionally?


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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 11:02 am 
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DKwan wrote:
I think the solving challenge should be completely different because on all of the "regular" crazy 4x4's, turning on the 2x2 cuts does not affect any circles, while on the double-circle 4x4 it would.

Each stickered surface on a Crazy 4x4x4 can be mapped to a Multi 4x4x4 as seen here for Type 3:
Image
Note there are still unstickered surfaces on some of the cubies that make up the Multi 4x4x4 but you only need two adjacent surfaces stickered on any given cubie to give it a unique position and orientation in the solved state. Here are links for the mapings for the other Crazy 4x4x4's:
http://wwwmwww.com/Puzzle/Crazy1.png
http://wwwmwww.com/Puzzle/Crazy2.png
http://wwwmwww.com/Puzzle/Crazy4.png

All but Type I are actually Super-Multi 4x4x4's. If you add more circles you can sticker more of the cubie surfaces on the Multi 4x4x4 but as you already have enough surfaces stickered to turn them into Super-Multi 4x4x4's (i.e. each pieces has a unique position and orientation in the solved state) then adding more stickers (or circular cuts) adds no new information.

If I was up to speed on the 4x4x4 notation I could probably even make the image showing the maping for this proposed puzzle rather easily. As is... I'm still not sure what layers you have tied to which circles. But regardless of how you have the circles designed to turn I see no way to add new information unless this is something along the lines of the Crazy Plus puzzles.
DKwan wrote:
Edit: Also Carl, are the "corners" of the outer-circles missing from your puzzle intentionally?

Yes. The piece that goes there is part of another piece already present on the puzzle. Can you tell me which one? That other piece (or pieces) already has a unique position and orientation so adding this "corners" while it does sticker a new face of a Multi 5x5x5 cubie it doesn't add any new information. So since it doesn't add anything new to the puzzle and as the puzzle would have to be a fair bit bigger to make room for a mech which would hold it in, I just decided to leave it off.

Carl

P.S. The above Double Circle 5x5x5 I posted above is NOT a Super-Multi5x5x5. It's just a Multi5x5x5. Can you tell me which piece (or pieces) don't have a unique position and orientation in the solved state? And which quality is that piece (or pieces) missing, a unique position or a unique orientation?

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 11:24 am 
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wwwmwww wrote:
If I was up to speed on the 4x4x4 notation I could probably even make the image showing the maping for this proposed puzzle rather easily. As is... I'm still not sure what layers you have tied to which circles. But regardless of how you have the circles designed to turn I see no way to add new information unless this is something along the lines of the Crazy Plus puzzles.

The way the circles are tied to the layers is the key. In fact, it is somewhat related to the crazy plus puzzles in that in a given state, not all circles can be turned relative to their faces. As I had mentioned, I think damo676767 mis-interpreted how the center-cuts of it would have to function with regards to the circles. A 2x2-turn on the double-circle 4x4 would only be able to turn a circle on one of the two halves of the puzzle. Because of this, the puzzle would not function symmetrically as the crazy 4x4's do.

This is why I said it is actually a combo of a circle 2x2 and a circle 4x4 rather than a combo of two types of circle 4x4's.

Edit: Hmmm... I dunno, maybe it is just an asymmetric subset of the multi-4x4? I have a difficult time visualizing if that is true...
Edit2: I was just now thinking of what a crazy 2x2 is... and I think it solves like a fused cube. You only have one cut in each direction, but you have to solve pieces which function like a 3x3x3. I'm not sure how exactly that would correspond over to the double-circle 4x4, but I think it is something more than just a subset of a multi-4x4.

wwwmwww wrote:
Yes. The piece that goes there is part of another piece already present on the puzzle. Can you tell me which one?

I'm going to guess the green edge pieces. I think it's the same as the crazy 4x4 type III.


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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 12:09 pm 
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DKwan wrote:
Edit: Hmmm... I dunno, maybe it is just an asymmetric subset of the multi-4x4? I have a difficult time visualizing if that is true...

If this is asymmetric then yes it may be more then just a Multi4x4x4. You may have to view this as a subset of the Multi5x5x5. In which case the two circles may certainly be adding something new.
DKwan wrote:
I'm going to guess the green edge pieces. I think it's the same as the crazy 4x4 type III.

You are correct.

Carl

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 12:17 pm 
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Your mention of the crazy plus 3x3's in this discussion makes me now wonder how else you would represent the puzzles of that set... Can they all be considered different subsets of a multi-nxn with only 2 turnable cuts in each direction?


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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 2:42 pm 
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DKwan wrote:
Your mention of the crazy plus 3x3's in this discussion makes me now wonder how else you would represent the puzzles of that set... Can they all be considered different subsets of a multi-nxn with only 2 turnable cuts in each direction?

Yes!! The Crazy Plus 3x3x3's are all subsets of different Multi5x5x5's which are bandaged to allow only 2 turnable cuts on each axis. I know this is talked about a bit in the thread about my Uniaxial 3x3x3 here:

http://twistypuzzles.com/forum/viewtopic.php?f=9&t=20321

Check out the picture posted by GuiltyBystander in the third post. I believe Andreas Nortmann was the first to map the Crazy Plus 3x3x3's to restricted Multi5x5x5's and some of that may also be in the above thread. I'm not sure, but I thought it was discussed elsewhere before that as well.

Carl

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 Post subject: Re: Double circle cubes
PostPosted: Thu Jun 09, 2011 2:43 pm 
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DKwan wrote:
Your mention of the crazy plus 3x3's in this discussion makes me now wonder how else you would represent the puzzles of that set... Can they all be considered different subsets of a multi-nxn with only 2 turnable cuts in each direction?
Yes. See another one of Carl's threads although he didn't realize that's what he was doing at the time. My post explains the transformation.
The Uniaxial 3x3x3 & the Biaxial 3x3x3 aka Anisotropic 3x3x3

Edit: Carl beat me

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