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 Post subject: Is the mixup cube an unbandaged Rubik's Cube?Posted: Tue Sep 03, 2013 7:44 am

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
And if so, is there a term for doctrinaire puzzles which can be unbandaged or bandaged into other doctrinaire puzzles?

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Tue Sep 03, 2013 8:13 am

Joined: Thu Dec 31, 2009 8:54 pm
Location: Bay Area, California
Jared wrote:
And if so, is there a term for doctrinaire puzzles which can be unbandaged or bandaged into other doctrinaire puzzles?

I'd say no. A related question is "Is the 3x3x3 a bandaged puzzle" because if the answer to that is "no" then the answer to your question is no.

It's true that some puzzles can be subsets of other puzzles but I wouldn't say it's correct to call one puzzle bandaged or bandaged just because it is closely related to another puzzle.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Tue Sep 03, 2013 8:22 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Yes, a Rubik's Cube can be unbandaged into a Mixup Cube. You don't even need to change the proportions, it just adds a few more extra pieces if you leave it as a 3x3x3.

There isn't any term for doctrinaire puzzles which can be unbandaged into other doctrinaire puzzles, because all of them can be. Usually it's done by adding axes though, instead of doubling an existing axis. There's no term for doubling an axis though.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Tue Sep 03, 2013 8:39 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Oh.. Now you've done it.. Now you've really done it! You've broken the space time continuum with your stupid question.

Did Erno really think.. `I know.. I've a great idea.. I'm going to bandage a Mixup Cube, and this will be my great invention!`

The Rubiks Cube is the definer of definers, the base puzzle, the one stability.. how can it now be a bandaged puzzle!!!!!

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PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
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Last edited by Burgo on Tue Sep 03, 2013 4:02 pm, edited 1 time in total.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Tue Sep 03, 2013 12:39 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
Bram wrote:
Yes, a Rubik's Cube can be unbandaged into a Mixup Cube. You don't even need to change the proportions, it just adds a few more extra pieces if you leave it as a 3x3x3.

Right, then it's a Mixup Plus Cube. I kind of think of those as pretty much the same thing even though they're not.

...Actually Burgo it's your fault, because if it wasn't for your videos I wouldn't know how to finish solving the Mixup Plus, and wouldn't have become fascinated by it.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 4:40 am

Joined: Tue Feb 08, 2011 3:17 am
Location: Australia
Thanks for the nice words Jared.. The Mixup Plus puzzle that really got my attention in the series was the Wormhole III. I didn't think it was going to be much, but it really was understated.. a CLASS puzzle!

_________________
1st 3x3 solve Oct 2010 (Even though I lived through the 80s).
PB 3x3 55sec Jan 2011 (When I was a kid 1:30 was speedcubing so I'm stoked).
1st 3x3 Earth (nemesis) solve Jan 2011 My You Tube (Now has ALLCrazy 3X3 Planets with Reduction)

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 7:06 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
Well, there is really no reason to not un-bandage the mixup cube itself,
i.e. there is no reason to not be able to mix up a center with a corner,
ultimately making all pieces interchangeable. To be more specific here,
this could happen when we only move 45 degrees each one of the outer
faces, to then continue with other moves.

Yes, that will require some "small" new changes (I am talking about a
spherical tendency here), but its shape can still remain a cube.

Hmmm... the total-freedom cube?

Pantazis

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 12:17 pm

Joined: Mon Mar 30, 2009 5:13 pm
*Every* puzzle can be unbandaged to form another puzzle. The ultimate puzzle you end up with is a ball/block of brown "clay", comprising individual coloured "atoms" that must be put back into an ordered arrangement ("solution") by twisting virtual layers.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 2:17 pm

Joined: Mon Nov 30, 2009 1:03 pm
kastellorizo wrote:
Hmmm... the total-freedom cube?

Attachment:

Freedom Cube - view 1.jpg [ 126.19 KiB | Viewed 1393 times ]

I have no clue about the mechanism.

Oskar

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 3:03 pm

Joined: Fri Dec 28, 2012 1:50 pm
Location: Near Las Vegas, NV
Oskar wrote:
kastellorizo wrote:
Hmmm... the total-freedom cube?

Attachment:
Freedom Cube - view 1.jpg

I have no clue about the mechanism.

Oskar

I think the mechanism could be made using a shell buildup from a fully unbandaged sphere 612. This would allow 45 degree turns on all sides. It only makes sense...

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Wed Sep 04, 2013 3:17 pm

Joined: Mon Mar 30, 2009 5:13 pm
Oskar wrote:
kastellorizo wrote:
Hmmm... the total-freedom cube?

I have no clue about the mechanism.

Oskar

Yeah, right, let's see how long it takes to pop up on Shapeways!

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If you want something you’ve never had, you’ve got to do something you’ve never done - Thomas Jefferson

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Thu Sep 05, 2013 4:59 pm

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
KelvinS wrote:
Oskar wrote:
kastellorizo wrote:
Hmmm... the total-freedom cube?

I have no clue about the mechanism.

Oskar

Yeah, right, let's see how long it takes to pop up on Shapeways!

Exactly! (I predict a couple of months maximum)

Pantazis

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Thu Sep 05, 2013 7:48 pm

Joined: Tue Aug 11, 2009 2:44 pm
Oskar wrote:
Attachment:
Freedom Cube - view 1.jpg

I have no clue about the mechanism.

I don't think that geometry quite works, does it? With the top turned 45°, it looks like pieces will interfere.

But I have no doubt you can figure out a mechanism.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Thu Sep 05, 2013 8:00 pm

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
You could apply a fudged version of David Pitcher's Octocube.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Fri Sep 06, 2013 12:52 am

Joined: Thu May 31, 2007 7:13 pm
Location: Bruxelles, Belgium
Oskar wrote:
kastellorizo wrote:
Hmmm... the total-freedom cube?

Attachment:
Freedom Cube - view 1.jpg

I have no clue about the mechanism.

Oskar

I'm afraid this doesn't work. Edges and corners on the sphere don't move on the same orbit around a face. Unlike 90º turns, compositions of 45º rotations around 3 perpendicular axes don't form a finite group.
If you allow 45º turns without any restriction tney make the puzzle divide into infinitely small pieces.

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Fri Sep 06, 2013 2:12 am

Joined: Mon Nov 30, 2009 1:03 pm
gelatinbrain wrote:
I'm afraid this doesn't work. Edges and corners on the sphere don't move on the same orbit around a face.
Fudging? Non-circular rails/grooves?

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Fri Sep 06, 2013 2:18 am

Joined: Fri Nov 05, 2010 2:20 am
Location: Wherever
Oskar wrote:
gelatinbrain wrote:
I'm afraid this doesn't work. Edges and corners on the sphere don't move on the same orbit around a face.
Fudging? Non-circular rails/grooves?

The thing here is that 'total freedom cube' is already fudged. Therefore there will not be infinite pieces. But the fudging may be too severe for a good mechanism. Thats up to you to find out

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Fri Sep 06, 2013 9:42 am

Joined: Fri Nov 04, 2005 12:31 am
Location: Greece, Australia, Thailand, India, Singapore.
An external mechanism for such a 45 degree spherical structure can work (ahem) externally,
simply by using a Cauliflower-like puzzle mechanism, this time not in 2D, but in 3D.

Imagine having a sphere with 26 little beads symmetrically distributed on it (in a similar
way the 26 pieces are arranged on a 3x3x3 cube), and we can use an external "racket"
which simulates the turning of each of the puzzles' 26-8 = 18 faces(!). (yeap, we are now
having a face per bead which exist in a center or edge position, as each and every one
of them can be regarded as the center of a face - it doesn't seem to work for corners,
as those pieces which are - temporarily - there, are surrounded by six, not eight pieces).

During the turning, each center remains stable (but we can orient it if we want), while
it moves all the rest of the eight neighbour bids by 45, -45, or 90 degrees. Then, we may
continue with another face, etc.

That said, such a model surely works for simulating a regular 3x3x3 with a cubic form (as it
also works for *any* regular cubic nxnxn with two(!) rackets too - this idea is not new for me).
But for the Total Freedom Cube, or rather, the Total Freedom Sphere, a spherical approach
as described above is needed. And if you really want a cubic Total Freedom cube, you will
need a pretty flexible (in terms of transformation) racket to deal with all those different
shapes that would pop up!

So... is anyone up for some multiple ball/bead spherical total freedom tennis?

Pantazis

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 Post subject: Re: Is the mixup cube an unbandaged Rubik's Cube?Posted: Fri Sep 06, 2013 1:37 pm

Joined: Thu May 31, 2007 7:13 pm
Location: Bruxelles, Belgium
Oskar wrote:
gelatinbrain wrote:
I'm afraid this doesn't work. Edges and corners on the sphere don't move on the same orbit around a face.
Fudging? Non-circular rails/grooves?

Maybe "non-circular rails" is an option. I have no idea what other 2 technical terms mean.
But I thought some mechanism to move pieces like the picture below while rotating is necessary(centers are colored green, edges blue and corners orange).
Attachment:

temp2.gif [ 11.08 KiB | Viewed 1115 times ]

I think solving-wise this is quite a new challenge.
Not only each piece can be put in any of 26 places but also can be rotated by 15º(26x24 orientations for each).

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