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 Post subject: Circle Skewb [with video]
PostPosted: Sun Nov 25, 2012 11:00 pm 
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Hello,

I'm proud to present you my latest puzzle: the circle skewb! Since I saw Eric Vergo's Dreidel Skewb, in the "Packages Just Arrived with Rare Puzzles" thread, and the comment after that says that it looked like a circle skewb, I wondered if it was possible to make one. The main problem is that on a normal circle puzzle, the center piece (the piece in the center of a turning axis attached to the core) is fixed, but on a skewb, only four of the eight axis are attached to the core, because it could not function otherwise. So the problem is to find a solution where all corners are fixed, but also not fixed at the same time to be able to move... :lol:

After four design (not prototyped, as they were obviously not working) I was able to find a solution. ( picture of the mechanism at the end).
Jaap sphere

VIDEO

Here are some pictures:
ImageImage
ImageImageImage
Mechanism: (blue : pieces fixed to the core, red : corners, yellow : face centers, green : circle parts)
Image

Video coming soon (currently being edited)

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Last edited by polymaker on Mon Nov 26, 2012 8:01 pm, edited 2 times in total.

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 Post subject: Re: Circle Skewb
PostPosted: Sun Nov 25, 2012 11:04 pm 
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Wow, impressive! Great job!

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 12:54 am 
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Looks fantastic! Thanks for posting the Jaap sphere view. That is a very fun way to try to understand the mechanism. Congrats. I am looking forward to the video.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:10 am 
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Very pretty!!


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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:11 am 
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polymaker wrote:
The main problem is that on a normal circle puzzle, the center piece (the piece in the center of a turning axis attached to the core) is fixed, but on a skewb, only four of the eight axis are attached to the core, because it could not function otherwise. So the problem is to find a solution where all corners are fixed, but also not fixed at the same time to be able to move... :lol:
So the corners aren't free to turn on their own... correct? If so nice!!! The circle 3x3x3 exposes the core of the puzzle so you are actually playing with all 27 cubies. The Skewb has two virtual cores. I suspect these new pieces expose those cores... but I'll have to think about this to be sure.

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:20 am 
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Wow, great puzzle. It looks like 3.2.20 on gelatinbrain (the attached image is the result of one twist around the yellow blue red corner, front and back view.), which is still different from the circle skewb here, because the pieces marked by "X" were not moving on 3.2.20 but moving here. So, is this the puzzle?

io, thanks for correcting me.


Attachments:
Image 000.png
Image 000.png [ 22.66 KiB | Viewed 4514 times ]


Last edited by schuma on Mon Nov 26, 2012 2:20 am, edited 1 time in total.
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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:46 am 
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wwwmwww wrote:
polymaker wrote:
The main problem is that on a normal circle puzzle, the center piece (the piece in the center of a turning axis attached to the core) is fixed, but on a skewb, only four of the eight axis are attached to the core, because it could not function otherwise. So the problem is to find a solution where all corners are fixed, but also not fixed at the same time to be able to move... :lol:
So the corners aren't free to turn on their own... correct? If so nice!!! The circle 3x3x3 exposes the core of the puzzle so you are actually playing with all 27 cubies. The Skewb has two virtual cores. I suspect these new pieces expose those cores... but I'll have to think about this to be sure.

Carl


Hey Carl! Can you explain what you mean by 2 virtual cores, or give a link to a relevant discussion? I'm out of my depth reading your post currently...

EDIT - comment to Schuma removed since his post has been updated.

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Last edited by JasonSmith on Tue Nov 27, 2012 1:59 am, edited 1 time in total.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 2:17 am 
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io wrote:
Schuma, that looks similar, but the circle is more circular in the gelatinbrain puzzle, hiding the face centers.


Oh sorry, I made an apparent mistake. Gelatinbrain 3.2.20 looks more similar. I've edited my previous post.


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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 5:26 am 
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NICE!
This is really an awesome new puzzle. Wow would I love to own one of those.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 7:05 am 
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VERY nice puzzle!!!
wwwmwww wrote:
polymaker wrote:
The main problem is that on a normal circle puzzle, the center piece (the piece in the center of a turning axis attached to the core) is fixed, but on a skewb, only four of the eight axis are attached to the core, because it could not function otherwise. So the problem is to find a solution where all corners are fixed, but also not fixed at the same time to be able to move... :lol:
So the corners aren't free to turn on their own... correct? If so nice!!! The circle 3x3x3 exposes the core of the puzzle so you are actually playing with all 27 cubies. The Skewb has two virtual cores. I suspect these new pieces expose those cores... but I'll have to think about this to be sure.

Carl
Carl, can you explain, please, how you count 27 cubies? I see 38 visible pieces. (8 corners, 24 circle segments, 6 faces).
I interpret the "two virtual cores" in the following way. On a normal Skewb only four corners are attached to the core. Here an additional core B is needed. Correct?

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 7:26 am 
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Very nice work! The corners being attatched to the core reminds me of Tom's Compy Skewb.

-Doug

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 8:44 am 
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Another interesting detail: as the skewb is a deep cut puzzle, adding the "crazy"(circle) feature to the skewb, it become similar to a circle 2x2. And on a circle 2x2, some centers are also fixed to a corner, because it could lead to misalignment of the hidden slice layer. But on my circle skewb, I didn't bandage a corner, because it would bandage one of the virtual core, so four of the corners would be "1" ( by 1 I refer to 0=piece in the circle don't move with a turn, and 1 is the opposite).
So on my puzzle, you can turn the two opposite faces (I mean the corners but not the corner inside the circle :lol: confusing...), but unlike the circle 2x2, the alignment of the hidden slice layer is much more apparent, as the piece in the circle are convex. It is easy to turn it with your hands.

P.S. I hope my English is clear enough :lol:

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 12:28 pm 
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Konrad wrote:
Carl, can you explain, please, how you count 27 cubies? I see 38 visible pieces. (8 corners, 24 circle segments, 6 faces).
io I'll get to your question in a second. Konrad, think of a 3x3x3 as cut with 2 planar cuts on each axis of rotation. You end up with 3x3x3=27 cubies. There are 4 types of cubies. There is 1 core cubie, 6 face center cubies, 12 edge cubies, and 8 corner cubies. 1+6+12+8=27 cubies. So how do we see these 27 cubies on a circle cube. Let's look at this picture.
Attachment:
Cricle3x3x3.jpg
Cricle3x3x3.jpg [ 108.68 KiB | Viewed 4294 times ]

The core is the 6 face centers, they never rotate so you can think of the core cubie as having all 6 faces stickered. This is piece type "1" as seen in the picture.
The face fenter is seen in the 4 circle edges which just rotate with 1 face turn. These face centers have 4 stickered faces, just the top face you normally see stickered isn't one of them. This actually turns them into "super" centers as their orientation is now important. This is piece type "2".
The edge cubie is seen there on the edge, but you also see 2 additional sides of this cubie as corners in the circles. So the edges actually have 4 faces stickers. This is piece type "3".
The corner cubies are your normal corner cubies with just 3 faces stickered. This is piece type "4".

Granted physically the face centers are made of 4 disjoint pieces and the edges are also made of 3 disjoint pieces but these groups can NOT be scrabled. They move as a single piece. So:
1*6=6 stickers on the center cubie
6*4=24 stickers on face centers
12*4=48 stickers on edges
8*3=24 stickers on coners
And:
6+24+48+24=102 which is what you get when you multiply 6 by 17, the number on sickers I count on a single face on the puzzle so this accounts for all the stickers seen on this puzzle.

Does that help?
Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 12:59 pm 
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io wrote:
Hey Carl! Can you explain what you mean by 2 virtual cores, or give a link to a relevant discussion? I'm out of my depth reading your post currently...
If you want to get into the details it boils down to this. If you take a cube and cut it with the 4 planer cuts seen on a Skewb you just end up with 6 faces and 8 corners. So 14 real pieces. However if you apply Andreas Nortmann's Analysis of twistability as detailed here you will find 16 possible pieces. The additional 2 pieces are the 2 virtual cores. I call them virtual as they don't have any real volume in the ideal picture. You can see that application of his analysis here. But it basically boils down to this, one of the cores is actually present as the core on any mass produced Skewb. The other core is the piece you would have if the other 4 coners were screwed into a piece that didn't rotate when those corners were turned on their axis. One way to make these virtual pieces present as real volumes in the same puzzle is seen here. This Circle Skewb MAY be another. I'm still not quite sure how this puzzle turns... but the more I read I'm not sure it turns the way I'd expect a Circle Skewb to turn. More on that in my next post.
io wrote:
Schuma, that looks similar, but the circle is more circular in the gelatinbrain puzzle, hiding the face centers.
I know this one wasn't directed at me but this comment makes no sense to me.

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:28 pm 
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wwwmwww wrote:
....Does that help?
Carl
Thank you Carl, I understand this related to the Circle 3x3x3. I thought your sentence
Quote:
The circle 3x3x3 exposes the core of the puzzle so you are actually playing with all 27 cubies.
was referring somehow directly to the Circle Skewb. Obviously it was meant as an example where a puzzle exposes its core piece(s)?
I hope that a video will make the Circle Skewb clearer to me.
In any case it is a very nice and interesting puzzle.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 1:42 pm 
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polymaker wrote:
But on my circle skewb, I didn't bandage a corner, because it would bandage one of the virtual core, so four of the corners would be "1" ( by 1 I refer to 0=piece in the circle don't move with a turn, and 1 is the opposite).
So on my puzzle, you can turn the two opposite faces (I mean the corners but not the corner inside the circle :lol: confusing...)
Yes, very confusing. I'm eager to see the video.
polymaker wrote:
P.S. I hope my English is clear enough :lol:
Your english is fine. You are just trying to describe something with words that isn't very easy to describe. A video I think would help alot. I basically see 3 ways this puzzle could turn.

(1) The Order=3 Circle Skewb... basically each axis has 4 layers which can turn, the two opposite cirle sections and the two opposite skewb layers in the center. Only 3 of these layers are independant. The other layer can be thought of as a rotation of the other 3 and a global rotation.

(2) The Order=1 Circle Skewb... As the Skewb is an Order=1 puzzle I feel this is the most fitting with the name "Circle Skewb". Being Order=1 that means there is only 1 degree of freedom per axis of rotation. If you turned one of the inner central skewb layers then the opposite circle section would turn with it while the circle section in that layer itself does not turn. Note a rotation of the other central skewb layer would be equivanent to a global rotation of the puzzle after the above turn. There is really only 1 independant layer of rotation per axis.

(3) The Order=2 Circle Skewb... This one is more compliacted to explain. It differes from the Order=1 skewb in that if you turned one of the inner central skewb layers then the opposite circle section would NOT turn with it while the circle section in that layer itself does not turn. To see what I mean compare Gelatinbrain 3.1.7 (your basic Circle 3x3x3) as seen here Image with Gelatinbrain 3.1.15 as seen here Image

Gelatinbrain 3.1.15 is an Order=3 puzzle, one order higher then your basic 3x3x3 which is Order=2 along with Gelatinbrain 3.1.7. On a normal 3x3x3 you only have 3 layers, 2 opposite faces and a slice layer. On Gelatinbrain 3.1.15 you have 4 layers per axis of rotation, you again have 2 opposite faces and a slice layer, but you also have the two opposite face circle centers which are tied together and move as one. Think of making rotation of two opposite faces and the slice layer between them on Gelatinbrain 3.1.15 and then follow that with a global rotation of the entire puzzle and you will see the 4th layer.

If I follow your description correctly (not sure that I am) I think you may have built the Order=2 Circle Skewb. If so that is probably the most interesting puzzle from a solving point of view. A Order=1 Circle Skewb I think would solve just as a normal Skewb, in that if you just solved the corners and the face centers then I think the circle pieces would automatically be solved. Note the virtual cores of the skewb physically behave as if they are attached to the corners. So if the corners are solved then both virtual cores must also be solved.

If this is actually an Order=1 puzzle and there are more then the 16 pieces identified by Andreas Nortmann's Analysis of twistability I'll be amazed but it is possible. Look at Timur's Clockwork 4x4x4. Its an Order=1 puzzle with more then the 8 corners found in a 2x2x2. I just don't think this is possible without the use of Gears or something similar.

Carl

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Last edited by wwwmwww on Mon Nov 26, 2012 3:42 pm, edited 1 time in total.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 2:07 pm 
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EDIT: Per schuma's remark, this puzzle is obviously NOT 3.2.20.

It's not entirely clear to me if this behaves like 3.2.20 or not. That is, when you turn a vertex, the corner that vertex is centered on does not turn. What happens to the opposite vertex? If you turn the puzzle around did the opposite side of the puzzle change at all?

Operating on the assumption that this puzzle is equivalent to Gelatinbrain's 3.2.20 then the circle pieces are attached in pairs like so:
Attachment:
crazyskewbfront_pairs.png
crazyskewbfront_pairs.png [ 104.8 KiB | Viewed 4203 times ]


They're the same pieces that you get on the Circle FTO and in some sense are equivalent to Pyraminx edges. They come in two orbits, each orbit with 6 of them.

The corners behave like 3-color corners on a Pyraminx (not the trivial tips) and also come in two orbits.

I think you could view this puzzle as two fused Pyraminx + Skewb Centers.

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Last edited by Brandon Enright on Mon Nov 26, 2012 3:31 pm, edited 1 time in total.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 2:11 pm 
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Konrad wrote:
I thought your sentence was referring somehow directly to the Circle Skewb.
Arg... sorry about that. I should have known something was off as I had no clue how you were counting 38 visible pieces. I figured there was some reason why you weren't counting the edges... and it turns out there was. I was looking at the Circle Cube and you were looking at this Circle Skewb. To me if this is an Order=1 Circle Skewb your 38 visible pieces must reduce to 16 pieces. The 14 pieces found in a normal Skewb and its 2 virtual cores. Without thinking about it too hard, I think 4 corners would group to represent 1 core and 3 of the "circle segments" would group to represent 1 corner of a normal Skewb. I can't quite do all the rotations necessary and keep track of the 38 pieces in my head to be 100% sure but that is what I'd expect. Just now not sure this is what I'm calling an Order=1 Circle Skewb. If this is higher order then I'd certainly expect it to have more then 16 pieces.

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 2:22 pm 
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bmenrigh wrote:
What happens to the opposite vertex? If you turn the puzzle around did the opposite side of the puzzle change at all?
If the answer is "no" I'm calling that an Order=2 Circle Skewb. If the answer is "yes" and the opposite vertex turns with the layer being turned I'm calling that an Order=1 Circle Skewb. Which is equivalent to Gelatinbrain's 3.2.20? I haven't yet fixed my issues with Gelatinbrain so I can't easily check. I'm going to guess Gelatinbrain's 3.2.20 is an Order=2 Circle Skewb as your description produces more the the 16 pieces I'd expect to find in the Order=1 Circle Skewb. Am I correct?

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 3:01 pm 
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wwwmwww wrote:
bmenrigh wrote:
What happens to the opposite vertex? If you turn the puzzle around did the opposite side of the puzzle change at all?
If the answer is "no" I'm calling that an Order=2 Circle Skewb. If the answer is "yes" and the opposite vertex turns with the layer being turned I'm calling that an Order=1 Circle Skewb. Which is equivalent to Gelatinbrain's 3.2.20?


On Gelatinbrain's 3.2.20 the opposite vertex does not move. I have a feeling this puzzle is identical to 3.2.20 because I suspect he would have photoed the extra movement if it were there.

I was about to argue with you about your order classification but after thinking about it some more I come to the same conclusion you do (3.2.20 == Order 2; Opposite vertex turning == Order 1).

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 3:08 pm 
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Looks to me like there is one twist per corner which only affects pieces which are seen to be affected in the image after one twist, though it's not clear. If so, I'd consider the pieces in terms of the master skewb call it an octahedral puzzle (yes, I know that tetrahedral and octahedral puzzles can be considered to be the same).


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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 3:36 pm 
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bmenrigh wrote:
I have a feeling this puzzle is identical to 3.2.20 because...
I'm sort of in the same boat. But for a different reason. What I'm calling Order=1 Circle Skewb I think would be a rather boring puzzle as it really doesn't offer any more then a normal Skewb.

That said... I think I'd personally rather have the Order=1 Circle Skewb as I don't see any way to make a mechanism for that puzzle that keeps everything inside the cube. Note my Augmented Skewb makes use of external bridges. So if there is a mechanism out there that can pull this off I'd LOVE to own it.

And if this is the Order=2 Circle Skewb or Gelatinbrain 3.2.20, this also reveals another very interesting oddity. Note its possible to make the Order=2 Circle Cube (Gelatinbrain 3.1.7). But I don't see any possible way make the Order=3 Circle Cube (Gelatinbrain 3.1.15). It's not an even/odd thing as it is possible to make a circle 4x4x4 which is an Order=3 puzzle. I wonder if this is somehow tied to real versus virtual cores. Maybe it is possible to make a physical version of Gelatinbrain 3.1.15... but I know if I say its impossible, half the designers will jump on it to prove me wrong. ;)

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 3:49 pm 
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wwwmwww wrote:
bmenrigh wrote:
I have a feeling this puzzle is identical to 3.2.20 because...
I'm sort of in the same boat. But for a different reason. What I'm calling Order=1 Circle Skewb I think would be a rather boring puzzle as it really doesn't offer any more then a normal Skewb.

Well I see now it it's 3.2.20 for the same reason schuma pointed out:
schuma wrote:
Wow, great puzzle. It looks like 3.2.20 on gelatinbrain (the attached image is the result of one twist around the yellow blue red corner, front and back view.), which is still different from the circle skewb here, because the pieces marked by "X" were not moving on 3.2.20 but moving here. So, is this the puzzle?
Attachment:
circle_skewb_not_3.2.20.png
circle_skewb_not_3.2.20.png [ 69.74 KiB | Viewed 4112 times ]


io, thanks for correcting me.


However, this image:
Attachment:
crazyskewb2turn.jpg
crazyskewb2turn.jpg [ 112.56 KiB | Viewed 4112 times ]


Shows that the opposite corner does not turn with each move. This is the same as the corner behavior on 3.2.20 after [RBD, UBR]:
Attachment:
3.2.20.png
3.2.20.png [ 15.42 KiB | Viewed 4112 times ]

Notice the corners match up.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 3:57 pm 
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bmenrigh wrote:
Well I see now it it's 3.2.20 for the same reason schuma pointed out:
Yes, I noticed your above edit in red just after I made my post.
bmenrigh wrote:
However, this image: <SNIP> Shows that the opposite corner does not turn with each move.
Nice!!! So it appears there are 2 ways one could make an Order=2 Circle Skewb. Very interestings... Are these two fundamentally different puzzles? I suspect that both may reduce to your two fused Pyraminx + Skewb Centers picture but the pieces may just map in different ways. I'm not sure...

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 4:14 pm 
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wwwmwww wrote:
bmenrigh wrote:
Well I see now it it's 3.2.20 for the same reason schuma pointed out:
Yes, I noticed your above edit in red just after I made my post.
bmenrigh wrote:
However, this image: <SNIP> Shows that the opposite corner does not turn with each move.
Nice!!! So it appears there are 2 ways one could make an Order=2 Circle Skewb. Very interestings... Are these two fundamentally different puzzles? I suspect that both may reduce to your two fused Pyraminx + Skewb Centers picture but the pieces may just map in different ways. I'm not sure...

The points are a very strange view of the same pieces on a Master Skewb:
Attachment:
crazyskewbfront_ms_correspondance.png
crazyskewbfront_ms_correspondance.png [ 119.98 KiB | Viewed 4073 times ]


Here is the "grip analysis" that shows this:
Attachment:
ms_point_grips.png
ms_point_grips.png [ 7.91 KiB | Viewed 4073 times ]


And here are the same grips and the same piece on the Circle Skewb:
Attachment:
crazyskewbfront_grips.png
crazyskewbfront_grips.png [ 104.5 KiB | Viewed 4073 times ]


And while I was making these images Gelatinbrain update his program with a copy of this puzzle :D Thank you Gelatinbrain!
Code:
The timestamp on http://users.skynet.be/gelatinbrain/Applets/Magic%20Polyhedra/joglx/polyhedra.jar was updated.
New date: Mon, 26 Nov 2012 20:47:13 GMT
New md5:  c579228c3796bc7c6909815bbeb24fa2

The new puzzles appear to be:
+3.2.25


EDIT:
And here is the same sequence [ULB', RBD, ULB, RBD&2, ULB', RBD', ULB, RBD'&2] performed on both a Master Skewb and Circle Skewb showing the same pieces being cycled:
Attachment:
master_skewb_3-cycle.png
master_skewb_3-cycle.png [ 13.32 KiB | Viewed 4054 times ]
Attachment:
3.2.25_3-cycle.png
3.2.25_3-cycle.png [ 14.4 KiB | Viewed 4054 times ]

Ignore the fact that the sequence also moves the Pyraminx corners on the Circle Skewb.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 4:35 pm 
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polymaker wrote:
ImageImage
Ok... These two pictures show the turning best for me. The first appears to be a single turn away from the solution. Think of it as I turned the blue/yellow/red circle corner and the layer directly under it doesn't turn but the rest of the puzzle does turn with that 4 piece circle area. With that picture of the turning you can see the second picture is just a turn of the red/blue/white circle corner away. And as bmenrigh just pointed out this is a fundamentally different puzzle then Gelatinbrain 3.2.20. Being Order=2 it makes sense that it turns out to be a subset of the Master Skewb.

By the way, I find it highly ironic that this puzzle was inspired by Eric Vergo's Dreidel Skewb, which also just happened to be the SAME subset of the Master Skewb.

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 4:43 pm 
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wwwmwww wrote:
By the way, I find it highly ironic that this puzzle was inspired by Eric Vergo's Dreidel Skewb, which also just happened to be the SAME subset of the Master Skewb.
The corners of this Circle Skewb are not equivalent to any piece type on or in the Master Skewb. It is interesting that the ellipse pieces are from a Master Skewb though.

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 4:53 pm 
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bmenrigh wrote:
The corners of this Circle Skewb are not equivalent to any piece type on or in the Master Skewb. It is interesting that the ellipse pieces are from a Master Skewb though.
My bad... I stand corrected. You are correct... this is a new piece type. I believe this is one of the many (I can't recall the exact number at the moment) of virtual pieces that appear when one applies Andreas Nortmann's Analysis of twistability to the Master Skewb. Very nice!!!

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 4:58 pm 
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I'm a bit confused... why is the puzzle order=2? I think it's order=3. Am I missing something?

Attachment:
circleskewb.png
circleskewb.png [ 102.83 KiB | Viewed 4002 times ]

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 5:34 pm 
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The layers are more like this:
Image

What I mean earlier is that the two layer "2" can move freely at the same time.
Turning one layer "2" doesn't affect the opposing vertex (layer "1")

The layer "3" is hidden and linked with the two opposite vertex of an axis.

So, turning a corner by hand turns the hidden layer and the opposite corner (impossible because of friction).

I hope it's more clear like that.

I'm remaking the video to answer to all of your questions. :D

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 5:43 pm 
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Coaster1235 wrote:
I'm a bit confused... why is the puzzle order=2? I think it's order=3. Am I missing something?
I thinks this is a definition thing. There are atleast 3 definitions of order commonly used on this site?

To me:
Order = the number of independant layers per axis of rotation

One of the other defintions:
Order = the number of layers per axis of rotation

So to me the 2x2x2 is Order=1, using this other definition its Order=2. I think you are using the "other definition".

There is a third group that uses this definition:
Order = the number of layers per face.

Using this last definition the 2x2x2 and the 3x3x3 are both considered Order=1.

As a result I generally try to define order in each thread that I use it in so people know which definition I'm using.

Carl

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 Post subject: Re: Circle Skewb
PostPosted: Mon Nov 26, 2012 5:50 pm 
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wwwmwww wrote:
bmenrigh wrote:
The corners of this Circle Skewb are not equivalent to any piece type on or in the Master Skewb. It is interesting that the ellipse pieces are from a Master Skewb though.
My bad... I stand corrected. You are correct... this is a new piece type. I believe this is one of the many (I can't recall the exact number at the moment) of virtual pieces that appear when one applies Andreas Nortmann's Analysis of twistability to the Master Skewb. Very nice!!!

Carl

Assuming I've applied Burnside's lemma correctly...

The number of unique piece types for a vertex turning cube (face turning octahedron) is:
? (((1*1)*2^8) + ((4*2)*2^4) + ((3*2)*2^2) + ((3*1) * 2^4) + ((6*1)*2^4)) / 24
% = 23

So there are 23 possible piece types for an order-2 VTC / FTO.

Some of these pieces will come in mirrored pairs (they will be chiral). If I've applied mirroring correctly then I count:
? (((1*1)*2^8) + ((4*2)*2^4) + ((3*2)*2^2) + ((3*1) * 2^4) + ((6*1)*2^4) + ((1*1)*2^4) + ((3*2)*2^1) + ((3*1)*2^2) + ((4*2)*2^2) + ((6*1)*2^4)) / 48
% = 15

So there are 15 fundamentally distinct pieces when you count chiral pieces as the same on an order-2 VTC / FTO. This means that there are 4 piece types that come in a right-and-left chiral version.

The corners of this Circle Skewb are one of these piece types. There are 8 of them in two orbits. Each has 3 orientations, all three are reachable.

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 Post subject: Re: Circle Skewb [with video]
PostPosted: Mon Nov 26, 2012 5:54 pm 
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I just want to say that I just saw in Brandon post that gelatinbrain added my puzzle (3.2.25), I updated and I confirm that the turning is the same as my puzzle.

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 Post subject: Re: Circle Skewb [with video]
PostPosted: Tue Nov 27, 2012 12:32 am 
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Hi,
These are the results of the "grip analysis" (bmenrigh) or "Analysis of twistability" (my term) for HC2
which is the cornerturning hexahedron with 3 logical layers.
Attachment:
HC2.png
HC2.png [ 9.08 KiB | Viewed 3840 times ]

Out of this set the Circle Skewb has
F3 (known from Skewb and Master Skewb)
X9 (known from Master SKewb)
Cz3 (a ZHP - ZeroVolumeHoldingPoint aka virtual piece)

For reference:
The naming scheme for the (normal) pieces is explained here
The three ZHPs are named with respect to a preliminary naming scheme for these pieces.
The second lower case latter (which can be different than z) denotes it is a ZHP.
The first letter C is given this piece shares the same symmetries as the "NonZeroVolume" C-pieces.
The letters H and Z denote these pieces have symmetries which are unknown in "NonZeroVolume" pieces.

This also answers another question of Carl.
There are 9 types of HoldingPointPieces in HC2 and 3 of them have ZeroVolume when only straight cuts are allowed.

Andreas

EDIT: Enhanced the description of the table.


Last edited by Andreas Nortmann on Wed Nov 28, 2012 12:27 pm, edited 1 time in total.

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 Post subject: Re: Circle Skewb
PostPosted: Tue Nov 27, 2012 1:59 am 
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wwwmwww wrote:
io wrote:
Schuma, that looks similar, but the circle is more circular in the gelatinbrain puzzle, hiding the face centers.
I know this one wasn't directed at me but this comment makes no sense to me.

Carl


I think this might be because you saw Schuma's post after he edited it to show 3.2.20. It was a different puzzle when I posted, which had different cuts which removed the face centers completely. I'll edit my comment now so it doesn't throw anyone off. Thanks for the reading material. Getting into it....

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 Post subject: Re: Circle Skewb [with video]
PostPosted: Tue Nov 27, 2012 1:50 pm 
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Andreas Nortmann wrote:
These are the results of the "grip analysis" (bmenrigh) or "Analysis of twistability" (my term) for HC2
which is the cornerturning hexahedron with 3 logical layers.
Thanks... this is what I was after. One question... I follow most of the naming you use. Most of that I follow from here. Basically the first letter of the name is one of the following:

O => A core
C => Corners
F => Faces
E => Edges
X => X-Faces
T => T-Faces
W => Wings
L => Obliques

If is a virtual piece or Zero Volume Holding Point you add a lower case 'z' and you add a number for the number of such pieces for the number of pieces moved in a single non-slice turn provided the number is greater then zero. I think we've said in the past this doesn't always produce a unique name but a simple example escapes me at the moment. So what do the 'H' and 'Z' mean for the parts in index positions 3 and 7? I need to dig out my mater skewb and perform those turns and see if I can conceptualize which piece is remaining stationary and that should answer the question for me but I can't do that in my head at the moment.

For everyone else, of the 9 pieces in Andreas' table the 6 that I call real (or non-virtual) can be seen in this animation:

Image

The numbers in the animation related to these names from the table.

0 = O (Core)
1 = C1 (Inner Corners)
2 = E3 (Edges)
3 = F3 (Faces)
4 = X9 (X-Faces)
5 = C4 (Outer Corners)

The other 3 pieces types I call virtial specifically because they do not show up in this animation. I need to check the piece counts bmenrigh produced above but I think those include all the imaginary pieces as well. But to go into that I'd get even farther off topic. Basically imaginary pieces are pieces that don't show up in Andreas' Analysis of twistability because they can't serve as holding points. I wouldn't expect them to show up in any circle puzzle... they are VERY tricky to bring into play in any real/physical puzzle.

Which reminds me of a question Andreas asked me at the last IPP... but I think I'll save that for another thread.

Carl

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 Post subject: Re: Circle Skewb [with video]
PostPosted: Wed Nov 28, 2012 12:29 pm 
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wwwmwww wrote:
So what do the 'H' and 'Z' mean for the parts in index positions 3 and 7?
I tried to answer the question in my previous posting which I edited for that purpose.


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