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 Post subject: Supergroup of the SeniorBarrel?Posted: Sun Jul 04, 2010 12:17 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
After I received some agreement, that the FusedCube is a doctrinaire puzzle and a subgroup of the 3x3x3 I came bakc to a long standing classification challenge of mine:
The Senior Barrel: viewtopic.php?f=15&t=16820

Question 1: Is there a shape transformation for this so its shape won't change under any move? In other words: Is it doctrinaire? I think yes.
Question 2: The 3x3x3 is a supergroup to the FusedCube where every gap between two pieces can be used for a move. What could the supergroup of the SeniorBarrel look like?

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Sun Jul 04, 2010 12:21 am

Joined: Sun Jun 13, 2010 1:00 am
That is a cool puzzle.

Question 1=a sphere

Question 2=I have no idea. Maybe a jumbling puzzle with 6 rotating sides instead of three?

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Sun Jul 04, 2010 12:30 am

Joined: Tue Sep 08, 2009 8:41 am
Location: The Blue Mountains, Australia
excuse my use of paint but wouldn't cutting along the red lines produce a puzzle where every gap between pieces could be used for a turn?
Attachment:

senior barrel.jpg [ 16.28 KiB | Viewed 3180 times ]
And would this not be kind of similar to a three layer hexagonal prism? If it were in that shape and fudged like Oscar's illegal cube i suppose you could get it to not change shape too.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Sun Jul 04, 2010 11:14 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
It's basically like the illegal cube, although I suspect it would involve a bit more fudging, because the no-fudge thing has four, the illegal cube has five, and the senior barrel has six. It wouldn't be necessary to make it have six slices though, three is just fine.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Sun Jul 04, 2010 11:30 pm

Joined: Tue Sep 08, 2009 8:41 am
Location: The Blue Mountains, Australia
Bram wrote:
It wouldn't be necessary to make it have six slices though, three is just fine.
I'm not exactly sure what you mean. No one mentioned 6 slices just 6 rotating sides (though counting top and bottom it would really be 8.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 10:19 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Thinking about it again I came up with this:

The shape of a hexagonal prism, not the puzzle known under this name.
Two cuts parallel to the hexagons.
Within every square of the prism there are circles (not interfering with each other)
The circles are cut into 9 segments comparable to the senior barrel
There are 2*3 cuts which go through the prism. These cuts are orthogonal to the square surfaces.

Interesting thing here is that this puzzle can retain its shape just because the circles don't interfere. Reminds me of Vergos cube...

Edit: Added some word to be more precise.

Last edited by Andreas Nortmann on Mon Jul 05, 2010 10:46 am, edited 1 time in total.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 10:28 am

Joined: Wed Jan 07, 2009 6:46 pm
Location: Evanston, IL
Andreas Nortmann wrote:
A hexagonal prism.

Exactly. I'll draw this up in solidworks and post it later today.

-π (Eitan)

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 11:01 am

Joined: Fri Mar 06, 2009 9:23 pm

I would view the senior barrel as a 1x1x3 in the shape of a triangular prism, with the "cross" idea as seen by Tony Fisher' cross cube applied to the square sides of the 1x1x3, but that's just me.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 11:20 am

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
Apparently no fudging necessary at all.

Boy do I feel dumb for not figuring that out.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 12:12 pm

Joined: Wed Jan 07, 2009 6:46 pm
Location: Evanston, IL
Oops! I guess I spoke too soon. Here's some proof that the hexagonal prism version of this puzzle wouldn't qualify for the non-shape-changing shape mod of the senior barrel:

Attachment:
File comment: Oops....

Full Senior Prism.JPG [ 76.16 KiB | Viewed 2997 times ]

Gingervergo has got the right idea. I'm so glad one of my puzzles is so tough to classify. It give you something to do in between collecting/making those complete sets, Andreas!

-pi (Eitan)

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 12:45 pm

Joined: Sun Jun 13, 2010 1:00 am
So for the supergroup, all cuts need to be extended. The resulting puzzle would jumble, maybe.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Mon Jul 05, 2010 11:41 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Thanks for your posts but I meant something else.
gingervergo shows a shape transformation of the Senior Barrel which prooves that it is doctrinaire but this is not a supergroup. I asked for a puzzle where every cut between two neighboring pieces can be used for a move without turning something beforehand.
On gingervergo's design one would have to apply at least the red and yellow (and the third set) cuts too. Maybe a hexagonal prism (the solid not the puzzle) with six of gingervego' square extensions will do the job.
Or one has to walk down the road Elwyn showed us...

 Attachments: Capture1.jpg [ 84.35 KiB | Viewed 2954 times ]
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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 12:30 am

Joined: Sun Jun 13, 2010 1:00 am
Andreas Nortmann wrote:
Thanks for your posts but I meant something else.
gingervergo shows a shape transformation of the Senior Barrel which prooves that it is doctrinaire but this is not a supergroup. I asked for a puzzle where every cut between two neighboring pieces can be used for a move without turning something beforehand.
On gingervergo's design one would have to apply at least the red and yellow (and the third set) cuts too. Maybe a hexagonal prism (the solid not the puzzle) with six of gingervego' square extensions will do the job.
Or one has to walk down the road Elwyn showed us...

That's what I kept saying. I just didn't have the fancy pictures

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 1:21 am

Joined: Tue Sep 08, 2009 8:41 am
Location: The Blue Mountains, Australia
PuzzleMaster6262 wrote:
That's what I kept saying. I just didn't have the fancy pictures
Yes but you also mentioned it might jumble and a jumbling puzzle by definition acts in a bandaged way at times and therefore not every cut could be used for a move after a turn so if it did jumble it couldn't be a super group.
PuzzleMaster6262 wrote:
Maybe a hexagonal prism (the solid not the puzzle) with six of gingervego' square extensions will do the job.
I don't see how that would be much different to this with illegal cube like fudging
Attachment:

hexagonal prism.jpg [ 52.65 KiB | Viewed 2931 times ]
unless you meant having gaps between the rotating sides like gingervirgo's picture which i suppose could also work actually not really because you need the rotating faces to overlap for it to be more like the senior barrel. Though after looking at it i do agree with bram that it would take more fudging than the illegal cube and possibly not really be possible... except for Oscar.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 9:01 am

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Elwyn wrote:
Yes but you also mentioned it might jumble and a jumbling puzzle by definition acts in a bandaged way at times and therefore not every cut could be used for a move after a turn so if it did jumble it couldn't be a super group.

Are you saying any jumbling puzzle isn't a super group? In the solved state of a 24-Cube every cut can be used for a turn. What is the definition of a super group? I'm thinking its any group that contains the group in question. Like the 2x2x2 is a sub-group of the 3x3x3 (its corners). The super group of a 2x2x2 could be a 3x3x3, a 4x4x4, etc.

Carl

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 9:10 am

Joined: Fri Feb 06, 2009 2:57 pm
Location: Pittsburgh
I think I understand the fudging used in the illegal cube, I'll try to draw something up when I have spare time for this.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 9:27 am

Joined: Tue Sep 08, 2009 8:41 am
Location: The Blue Mountains, Australia
wwwmwww wrote:
Are you saying any jumbling puzzle isn't a super group? In the solved state of a 24-Cube every cut can be used for a turn. What is the definition of a super group? I'm thinking its any group that contains the group in question. Like the 2x2x2 is a sub-group of the 3x3x3 (its corners). The super group of a 2x2x2 could be a 3x3x3, a 4x4x4, etc.
I took Andreas to mean a super group was able to use any gap between pieces as a move after any complete turn not just in the solved state. But perhaps that's not what he meant as i was just going on what was said in this thread and intuition Also all gaps on a 2x2 can be used for turns so it is the super group of all the bandaged 2x2 variants i suppose and there doesn't need to be a super group of it. other wise all nxnxn cubes would have a super group of infinityXinfinityXinfiinity

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 12:15 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
"supergroup" is just the opposite term of "subgroup". There are many supergroups. So yes the 3x3x3 is a supergroup of the 2x2x2. And a jumbling puzzle might be the supergroup to another puzzle. The interesting question here is wheather the subgroup is always jumbling when the supergroup isn't. But please leave that question to another thread.

I asked for the supergroup with the properties elwyn restated.
I came up with an ugly sketch about what I meant. Please note that this is just the topview.
Attachment:

Topview.jpg [ 28.88 KiB | Viewed 2872 times ]

No fudging needed!
If I had drawn the squares smaller then they would not interfere with each other.

What made it so challenging for me to classify the senior Barrel was the fact that it is no member of the 6+N "traditional" classes of twisty puzzles since it allows 90° turns where only 180°-ones should be allowed.
I think these puzzles outside of the "traditional" classes can only be implemented with the help of:
1. fudging (e.g. the illegal cube)
or
2. no interference between the movements which are beyond the classic scope. (e.g. pipe connector).

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 8:13 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Here you go...

Attachment:

Thing.png [ 99.93 KiB | Viewed 2843 times ]

A 20 sided Polyhedron formed of 2 hexagons, 6 squares, and 12 right triangles. Is there a name for this shape?

Carl

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 8:15 pm

Joined: Sun Jun 13, 2010 1:00 am
wwwmwww wrote:
Here you go...

Attachment:
Thing.png

A 20 sided Polyhedron formed of 2 hexagons, 6 squares, and 12 right triangles. Is there a name for this shape?

Carl

Perfect
But it doesn't jumble

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Tue Jul 06, 2010 8:57 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
gingervergo wrote:

This puzzle should be made in the shape of a triaugmented triangular prism.

http://mathworld.wolfram.com/TriaugmentedTriangularPrism.html

There are only eight convex deltahedra. We see the 3 regular ones all the time. And I think Bram was the first to use one of the other 5 with his puzzles based on the geometry of the triangular dipyramid. Here is another nice link.

http://www.ac-noumea.nc/maths/polyhedr/p_delta_.htm

So the nicest answer to the question:

Quote:
Question 1: Is there a shape transformation for this so its shape won't change under any move?

My vote is for the triaugmented triangular prism. I can't say that is the shape that popped into my head when I first read the question but it works.

Carl

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Wed Jul 07, 2010 12:24 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Yes, Carl. That is what I have thought of.
wwwmwww wrote:
Is there a name for this shape?
I would go for HexaugmentedHexagonalPrism but don't know for sure.
PuzzleMaster6262 wrote:
But it doesn't jumble
Even more perfect. Thats my opinion.

Now the next challenge. We have found the "cutting through everywhere"-supergroup of the SeniorBarrel. What is the "cutting through everywhere"-supergroup of the pipe connector?

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Wed Jul 07, 2010 7:45 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
Now the next challenge. We have found the "cutting through everywhere"-supergroup of the SeniorBarrel. What is the "cutting through everywhere"-supergroup of the pipe connector?

Nice!! Now that I know the trick its easy. Its this solid cut with 21 cutting planes.

Attachment:

Pipe.png [ 170.36 KiB | Viewed 2767 times ]

This means the Pipe Connector is a pure twisty puzzle with no slidey parts. Cool! The red box in the center DOESN'T turn like a 4x4x4 by the way. The 15 cut planes in the red box go through the center of the puzzle. The other 6 cut planes run along the surface of the red box so the green pieces can rotate on their own. Building or even playing with this puzzle would be a nightmare as this puzzle can jumble like crazy.

Carl

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Wed Jul 07, 2010 9:44 pm

Joined: Mon Aug 18, 2008 10:16 pm
Location: Somewhere Else
I'd like to see a "plain" version of that one some day!

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Thu Jul 08, 2010 10:15 am

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Cool, Carl!
Very impressing!

and quite interesting:
1. The "cutting through everywhere"-supergroup of the pipe connector is jumbling.
2. The "cutting through everywhere"-supergroup of the Senior Barrel is NOT jumbling.
Even more interesting since both are out of the scope of "traditional" classes of twisty puzzles.

This must be a result of this: For 1. We have the hexagonal prism (the solid) we can rely on. For 2. there is not shape which could stop (?) it from jumbling.

I thought after "cutting through everywhere" there were just two classes of puzzles: Those which jumble and those "traditional" 6+N ones.
Seems like there is a third class...

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Thu Jul 08, 2010 7:11 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
Even more interesting since both are out of the scope of "traditional" classes of twisty puzzles.

Define "traditional"? Looks like we are now trying to break the "pure" twisty puzzles into subgroups.

Andreas Nortmann wrote:
I thought after "cutting through everywhere" there were just two classes of puzzles: Those which jumble and those "traditional" 6+N ones.
Seems like there is a third class...

I agree with the jumbling and non jumbling classes. Not sure what you mean by 6+N ones. I guess you could also break up twisty puzzles into various symmetry groups which is what it sounds like you are doing.

I'm not sure this helps but the "cutting through everywhere"-supergroup of the pipe connector I presented isn't the only one. You could extend the green area to make it a cube that encloses the red cube and just extend the cut planes. A nice looking example of this would be to take the red cube and add the 4x4x4 cut planes at the locations where it already "appears" they are. This puzzle would also be a supergroup of the pipe connector and look like a "normal" cube. It adds MANY pieces that you don't need in the simplier puzzle I presented above (which is already so complex I never expect to see it built) but maybe the strait cube version might fit your definition of "traditional". I'm not sure.

Carl

P.S. Now that I have said that I'm not so sure. Is this FULL cube version really a supergroup of the Pipe Connector? The puzzle above made with a subset of its pieces IS. But in retrospect I think there is a good chance that the extra pieces contained in the cubical puzzle which would jumble by a 30 degree rotation of a face would eventually BLOCK a rotation that is allowed on the Pipe Connector and the simplier supergroup puzzle pictured above. Actually I'm sure of it. Rotate one 4x4x4 face by 30 degress now the only other 4x4x4 face that is free to rotate is the opposite one. All adjacent face rotations are blocked. Since the full puzzle CAN'T make a move that Pipe Connector CAN I don't consider the Pipe Connector a subset of this puzzle which I think kills its supergroup status. I find it interesting that a subset of the pieces of a puzzle can make a puzzle that isn't a subset of the original puzzle. I think this is only true of jumbling puzzles. I think this is akin to why a helicopter sphere (a shape mod of a helicopter cube) is actually a different puzzle then a helicopter cube... there are jumbling moves allowed on one that aren't on the other.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Fri Jul 09, 2010 12:56 pm

Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
6+N was a reference to:
Face/Corner/Edge-turning dodecahedron/hexahedron (and the hybrids) plus N-gonal prisms (this time NOT the solids) with 180° turns.
wwwmwww wrote:
I'm not sure this helps but the "cutting through everywhere"-supergroup of the pipe connector I presented isn't the only one.
I am sure about that but this supergroup will be jumbling too. Won't it?

In your PS you have discovered, that your supergroup does work only when the green pieces don't interfere with each other. That was the case for the supergroup of the SeniorBarrel, too. You had to flatten the extensions on every square to achieve that.
This property "works only without interference or with fudging" seems to discriminate all these puzzles from the 6+N traditional ones.

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 Post subject: Re: Supergroup of the SeniorBarrel?Posted: Fri Jul 09, 2010 1:11 pm

Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
6+N was a reference to:
Face/Corner/Edge-turning dodecahedron/hexahedron (and the hybrids) plus N-gonal prisms (this time NOT the solids) with 180° turns.

Thanks.

Andreas Nortmann wrote:
I am sure about that but this supergroup will be jumbling too. Won't it?

Yes.

Andreas Nortmann wrote:
In your PS you have discovered, that your supergroup does work only when the green pieces don't interfere with each other. That was the case for the supergroup of the SeniorBarrel, too. You had to flatten the extensions on every square to achieve that.
This property "works only without interference or with fudging" seems to discriminate all these puzzles from the 6+N traditional ones.

Interesting observation. I'm not sure what to make of it just yet. In both cases we have basically added a few 2D pieces to the face of a 3D puzzle and we aren't allowing the 2D pieces to interfere with each other across faces. Sure we can give the 2D pieces volume as long as they still don't interfere but I think its the 2D nature of these pieces that causes them to fall outside your classes.

Carl

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