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 Post subject: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Tue Jul 31, 2012 1:04 pm 
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Hi,

this is another batch of 3x3x3-variants.
Their common property is that they do not behave like bandaged puzzles.
For all of these variants one can give a subset of moves of the 3x3x3 which defines the possible moves of the variant.
Compared with this thread:
viewtopic.php?f=14&t=15016
this time restrictions to halfturns are included.

The ten new variants are:
Bandaged 3x3x3: C000060 <U D L R2>
Bandaged 3x3x3: 18C000060 <U D2 L R2>
Bandaged 3x3x3: F7A00108 <U D2 L2>
Bandaged 3x3x3: 42000B5A00108 <U2 D2 L>
Bandaged 3x3x3: 202005AD <U F Fs2>
Bandaged 3x3x3: 42000000005AD <U F2 Fs>
Bandaged 3x3x3: 42000202005AD <U F2 Fs2>
Bandaged 3x3x3: 738005AD <U2 F Fs2>
Bandaged 3x3x3: C000C00 <L F Ls2 Fs2>
Bandaged 3x3x3: 18C600C00 <L F2 Ls2 Fs2>
Please note that the specially marked faces mean that the face is strongly connected to the core.

In total I identified 22 subgroups
which can be defined as subgroups of twistybility
which definition include halfturns
which can be implemented with traditional bandaging
which have at least two turnable adjacent sides.

Some (like the Quadromese cube) I already implemented years ago.
Some (like the Floppy Cube or the slim cube) are available als massproduced or 3D-printed puzzles.
3 subgroups are trivial because they are subgroups of the Floppy Cube.
The remaining ten were missing until now.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Wed Aug 01, 2012 12:30 am 
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I love the precision you fill up long time open slots.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Wed Aug 01, 2012 10:52 am 
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Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Did you include the one where one face center is glued to two opposite edges, and the opposite face center can't rotate in place? That one is greater than deep cut.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Wed Aug 01, 2012 12:34 pm 
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Joined: Mon Aug 02, 2004 7:03 am
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Thank you Claus.

@Bram: Do you mean the attached variant? Orange is opposite to red.
I don't see how that one does not behave bandaged.
I can't find a subset of twistability in the form of <L F Ls2 Fs2> for it.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Wed Aug 01, 2012 3:26 pm 
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Location: Marin, CA
Andreas Nortmann wrote:
@Bram: Do you mean the attached variant? Orange is opposite to red.
I don't see how that one does not behave bandaged.
I can't find a subset of twistability in the form of <L F Ls2 Fs2> for it.


It's more than deep cut :-) Let's say that XU is 'Big U' and refers to turning both the top and the center slices in tandem while leaving the bottom unmoved. Then this one is <XU F B>. As you pointed out to me previously, the barbell cube is doctrinaire for similar reasons, although that involves center slices, not super-deep slices.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Thu Aug 02, 2012 2:26 pm 
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Okay. Now I understood.
I haven't built that one but I will change it.

By the way: Jaap tells us that variant has 327,666,691,473,408,000 permutations.
You can find it here
http://www.jaapsch.net/puzzles/subgroup.htm
in the third table under 3r. Jaaps calls that "Wide moves".

Are there other implementable subgroups with "Wide moves" or "super-deep slices"?


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Fri Aug 03, 2012 10:47 am 
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Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Andreas Nortmann wrote:
By the way: Jaap tells us that variant has 327,666,691,473,408,000 permutations.
You can find it here
http://www.jaapsch.net/puzzles/subgroup.htm
in the third table under 3r. Jaaps calls that "Wide moves".

Are there other implementable subgroups with "Wide moves" or "super-deep slices"?


From that table: 2c, 2e, 2f, 3x, and 4l (that's <Uw, R, F, L> there's a labelling problem where there are some collisions). I *think* that's it, but I could be missing something.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Sat Aug 04, 2012 4:27 am 
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2c is a bandaged 1x3x3 and therefore considered trivial.
2e was implemented years ago by me. Time to rediscover it.
2f, 3x and 4l are new and worth to be built.

Thank you


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Sat Aug 04, 2012 9:20 pm 
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Bram wrote:
Andreas Nortmann wrote:
@Bram: Do you mean the attached variant? Orange is opposite to red.
I don't see how that one does not behave bandaged.
I can't find a subset of twistability in the form of <L F Ls2 Fs2> for it.


It's more than deep cut :-) Let's say that XU is 'Big U' and refers to turning both the top and the center slices in tandem while leaving the bottom unmoved. Then this one is <XU F B>. As you pointed out to me previously, the barbell cube is doctrinaire for similar reasons, although that involves center slices, not super-deep slices.

I just built this variant and have been puzzling over it for the past two days. It's ridiculously difficult and I can safely say that I'm completely confused.

I would appreciate some hints regarding the solution. Simple commutators and conjugates have been failing me. :|

Chandler

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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Sun Aug 05, 2012 4:38 am 
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Quirky-Cubes wrote:
I would appreciate some hints regarding the solution. Simple commutators and conjugates have been failing me. :|
I would be glad to help but I am out of the solving-business.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Sun Aug 05, 2012 12:51 pm 
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Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Quirky-Cubes wrote:
Bram wrote:
It's more than deep cut :-) Let's say that XU is 'Big U' and refers to turning both the top and the center slices in tandem while leaving the bottom unmoved. Then this one is <XU F B>. As you pointed out to me previously, the barbell cube is doctrinaire for similar reasons, although that involves center slices, not super-deep slices.

I just built this variant and have been puzzling over it for the past two days. It's ridiculously difficult and I can safely say that I'm completely confused.

I would appreciate some hints regarding the solution. Simple commutators and conjugates have been failing me. :|


First position the DLB, DLF, DL, UF, and UB cubies. Next you'll view the cube from the point of view of the <Uw2 R> subgroup. Then use Uw R- Uw2 R Uw2 R Uw2 R- Uw to orient the corners and and Uw- R- Uw2 R- Uw2 R Uw2 R Uw- to orient the edges. Then position the corners, and finally position the edges using (R2 Uw2)6.


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 Post subject: Re: Bandaged 3x3x3s which don't behave bandaged
PostPosted: Tue Aug 07, 2012 7:34 pm 
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Thanks, Bram. I was able to solve it, and am now trying to construct a guide for it. (mainly for personal reference, but I can post it here when I get back from vacation.)

Chandler

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