All,

The Augmented Skewb is the puzzle that results when you apply Andreas Nortmann's Analysis of Twistability to the Skewb. His analysis reveals two additional pieces aside from the corners and faces present on typical Skewbs. This puzzle incorporates both as stickered pieces and presents a truly unique view of the Skewb.

Four days ago I finished a design for the Augmented Skewb that I presented here. At the time I hadn't even finished the sticker template. That was a day or two later. My model now looks like this. But that is not what I'm here to share with you today. In what is a personal record for me, I'm here to present the finished puzzle. From finishing the design to a functional and stickered puzzle in 4 days. WOW!!! This will very very soon be available for sale... want to guess where? Edge length is 60mm.
Weight is 111.9gm.

The Video is now up:
https://youtu.be/VEjprILJVUY

The Augmented Skewb is available here:
http://www.chewiescustomstickers.com/ca ... zzles.html

Enjoy,
Carl

P.S. Post edited to add weight and link to shop where puzzle is available. Video still coming soon.

From design to 3D-printed finished puzzle in four days?! Wow o.Ô

Nice job! And I'm looking forward to the video.

Greetz,
Quuador

Incredibly fast from CAD files to physical model! The pieces look like they've been sanded, or tumbled (which wouldn't be possible in such a short time frame), or otherwise polished. Is it an FDM print that you've sanded? Do you now have an FDM printer at home?

On a different note, I love the color scheme you've used. The puzzle looks beautiful. Can't wait to see the video!

David Pitcher wrote:Incredibly fast from CAD files to physical model! The pieces look like they've been sanded, or tumbled (which wouldn't be possible in such a short time frame), or otherwise polished. Is it an FDM print that you've sanded?

Yes and No... in that order.

David Pitcher wrote:Do you now have an FDM printer at home?

No... but the person who sanded the puzzle does.

David Pitcher wrote:On a different note, I love the color scheme you've used.

Again that credit shouldn't go to me. I simply provided a sticker template. My rendered model has the typical white opposite yellow, red opposite orange, and green opposite blue with red, white, and blue appearing in clockwise order on one corner.

David Pitcher wrote:The puzzle looks beautiful. Can't wait to see the video!

Thanks!!! And I'm certain the stickerer (is that a word) thanks you too. All should be made clear in a couple hours.

Carl

Is that an FDM print by Chewie?
I can't wait for the video

jiroscop wrote:Is that an FDM print by Chewie?
I can't wait for the video

Yep. Video is coming soon

chewbacca wrote:

jiroscop wrote:Is that an FDM print by Chewie?
I can't wait for the video

Yep. Video is coming soon

Looks like you have the answer. Here is the thread Chewie started:

http://twistypuzzles.com/forum/viewtopi ... =4&t=31615

And my new shop as well:

http://www.chewiescustomstickers.com/ca ... zzles.html

I'm just amazed at how fast this whole process has been. If you order now you may have one of these in your hands before I do and just the taught of that being possible has me grinning from ear to ear.

Chewie, do you have a scale? Just curious if we can provide a weight for Andreas.

Thanks,
Carl

wwwmwww wrote:Chewie, do you have a scale? Just curious if we can provide a weight for Andreas.

Thanks,
Carl

I have one at work. I will weigh it tomorrow.

wwwmwww wrote: But that is not what I'm here to share with you today.l

Huh?
Are you kidding me. You present this achievement and that is not the main point?

Amazing.
Has somebody already calculated the number of permutations?

I forgot to bring the puzzle to work. I will get its weight tomorrow.

Andreas Nortmann wrote:Huh?
Are you kidding me. You present this achievement and that is not the main point?

I'm old school. I consider the New Puzzle section of the forum devoted to new puzzles, not new renders. Just my point of view.

Andreas Nortmann wrote:Amazing.
Has somebody already calculated the number of permutations?

Is that a rhetorical question? Yes, I am certain many have calculated the number of permutations. Jaap for example:
https://www.jaapsch.net/puzzles/skewb.htm
Depending on how its stickered you could get any of these numbers as well:
https://www.jaapsch.net/puzzles/ultimate.htm

Am I missing something?

Carl

wwwmwww wrote:

Andreas Nortmann wrote:Amazing.
Has somebody already calculated the number of permutations?

Is that a rhetorical question? Yes, I am certain many have calculated the number of permutations. Jaap for example:
https://www.jaapsch.net/puzzles/skewb.htm
Depending on how its stickered you could get any of these numbers as well:
https://www.jaapsch.net/puzzles/ultimate.htm

Am I missing something?

Carl

If you're implying that the number of permutations is the same as the normal Skewb, just say that. It's not at all obvious that the two are equivalent.

themathkid wrote:If you're implying that the number of permutations is the same as the normal Skewb, just say that. It's not at all obvious that the two are equivalent.

Yes. I believe this puzzle has exactly the same number of permutations as a normal Skewb. However I now have to add a small caveat. I certainly would have expected Andreas to know that. Since he asked the question, I'm now second guessing myself.

But I certainly believe that if you can solve a Skewb then you should be able to solve this puzzle. Half the battle will be in identifying which piece on this puzzle maps to the corresponding piece on a normal Skewb.

Think of the relationship between a Circle Cube and a Stefan Pochmann 3x3x3. These are two equivalent puzzles too. And why couldn't I find the Stefan Pochmann 3x3x3 in the museum?

Carl

themathkid wrote:If you're implying that the number of permutations is the same as the normal Skewb, just say that. It's not at all obvious that the two are equivalent.

No it isn't obvious at all.

I've highlighted some pieces to show what they are: The three red corners are three of the four Skewb corners in one orbit. The three light-blue pieces together form one of the Skewb corners in the other orbit. You can one part of each of the other three corners in that orbit.

• The yellow corners together form the core.
• The green corners together form the anti-core.
• The hourglass pieces are the usual Skewb face pieces.

All there really is to show is that the anti-core doesn't add any positions. One possibility is that its orientation is fully determined by the the orientation and position of the two orbits of the Skewb Corners. Another possibility would be that it form the Klein-4 group. It isn't obvious to me which is correct. I'd have to check by either exploring the puzzle or with GAP.

Brandon Enright wrote:

• The yellow corners together form the core.
• The green corners together form the anti-core.

Which is the core and which is the inverse core is sort of ambiguous. You could also hold the puzzle by the green corners and consider that the core while allowing the yellow corners to move with every turn and thus represent the inverse core.

Brandon Enright wrote:One possibility is that its orientation is fully determined by the the orientation and position of the two orbits of the Skewb Corners.

Each cores orientation is completely determined by the position of just one of the orbits. The other orbit determines the other cores orientation. The orientation of the pieces in the orbits isn't needed. Just as you don't need to know the orientation of the face centers to determine the orientation of the core inside a 3x3x3.

Brandon Enright wrote:Another possibility would be that it form the Klein-4 group. It isn't obvious to me which is correct. I'd have to check by either exploring the puzzle or with GAP.

Ok... I now need to go look up what a Klein-4 group is but even without knowing I find it funny that you do and still don't know which answer is correct. The answer is obvious to me but it certainly helps that I designed it. LOL!!!

Carl

wwwmwww wrote:

Brandon Enright wrote:

• The yellow corners together form the core.
• The green corners together form the anti-core.

Which is the core and which is the inverse core is sort of ambiguous. You could also hold the puzzle by the green corners and consider that the core while allowing the yellow corners to move with every turn and thus represent the inverse core.

Yeah which is why I chose one of the two options because any answer we get out of one choice will be equivalent to the answer we get from the other choice.

wwwmwww wrote:

Brandon Enright wrote:One possibility is that its orientation is fully determined by the the orientation and position of the two orbits of the Skewb Corners.

Each cores orientation is completely determined by the position of just one of the orbits. The other orbit determines the other cores orientation. The orientation of the pieces in the orbits isn't needed. Just as you don't need to know the orientation of the face centers to determine the orientation of the core inside a 3x3x3.

Yeah I came to the same conclusion. The inverted core doesn't add anything.

Am I the only one who's going to ask if the circle pieces can be bandaged to come out of orbit like a crazy puzzle?

Burgo wrote:Am I the only one who's going to ask if the circle pieces can be bandaged to come out of orbit like a crazy puzzle?

Hmmm... Do you mean Crazy Plus? To me Crazy = Circle.

Also bandaged to me means to add a restriction. If that is what you want I would consider it removing a restriction, so unbandage might seem more appropriate. Not that I consider this a bandaged puzzle. It is doctrinaire as presented.

Anyways... assuming I understand the question correctly the answer is yes. You could free up 1, 2, 3 or all 4 circle corners and allow them to rotate and make the Crazy Plus versions of this. If I were to do that I'd likely want to make the circles a little larger such that they cut into the the other 4 corner pieces. This would create more pieces to solve. But these puzzles would be equivalent to the Crazy Tetrahedrons. Hmmm... I see they dropped the word Plus too. So I guess that means the term Crazy is rather ambiguous in this context now.

Carl

Brandon Enright wrote:The inverted core doesn't add anything.

Ok. I admit that question was shortsighted.

Just finished my animation. Slower then it took Chewie to make the actual puzzle. LOL!!!

Carl

wwwmwww wrote:Just finished my animation. Slower then it took Chewie to make the actual puzzle. LOL!!!

AugmentedSkewb.gif

Carl

I actually made 2 of them already.
Tech info for Andeas. Weight 111.9gm

wwwmwww wrote:

Burgo wrote:Am I the only one who's going to ask if the circle pieces can be bandaged to come out of orbit like a crazy puzzle?

Hmmm... Do you mean Crazy Plus? To me Crazy = Circle.

Also bandaged to me means to add a restriction. If that is what you want I would consider it removing a restriction, so unbandage might seem more appropriate. Not that I consider this a bandaged puzzle. It is doctrinaire as presented.

Anyways... assuming I understand the question correctly the answer is yes. You could free up 1, 2, 3 or all 4 circle corners and allow them to rotate and make the Crazy Plus versions of this. If I were to do that I'd likely want to make the circles a little larger such that they cut into the the other 4 corner pieces. This would create more pieces to solve. But these puzzles would be equivalent to the Crazy Tetrahedrons. Hmmm... I see they dropped the word Plus too. So I guess that means the term Crazy is rather ambiguous in this context now.

Carl

I've always (probably incorrectly, because I understand what you're saying about nomenclature) referred to (and thought of) the crazy bandaging as a type of `temporary bandaging`. The Jing's version of the Skewb in the Crazy Tets lacks the orientation of one of the cores (in reality the physical core), and the associated Inner Edges would be associated with different faces (you've called them `circle corners`, but on the Crazy Tets we've called them `Inner Edges`.. the CCs would be the additional pieces you would expose with larger circles.. just to add confusion).

Anyway, it's probably more of a conceptual puzzle in reality as well. You're right, it wouldn't be a huge solving challenge to add the Crazy Plus bandaging to the Circle Pieces (whatever we call them here). I really like seeing your work physically visualising concepts.

chewbacca wrote:Tech info for Andeas. Weight 130.41gm

Thanks.

Wow Carl.... that is very impressive!

Love the unique way of external bandaging, in my opinion, it is one of the best ideas to be realised.




Pantazis

The Video is now up.
https://youtu.be/VEjprILJVUY

Enjoy,
Carl

This is like an alien form coming to Earth to mimic humans, I mean...cubes. Fantastic. The principles and the reasoning to come up with this puzzle, dedication, design... just congrats to both Carl and Andreas for such a piece, and to chewbacca for making it possible.

What a team!

Roth wrote:This is like an alien form coming to Earth to mimic humans, I mean...cubes. Fantastic. The principles and the reasoning to come up with this puzzle, dedication, design... just congrats to both Carl and Andreas for such a piece, and to chewbacca for making it possible.

What a team!

Andreas and Carl, especially Carl have alien thought processes

If you read through Carl's recent Complex NxNxN posts and read past discussion threads you'll start to see how the thought process of holding points and symmetry between halves leads towards ideas like this puzzle. For example on the Skewb there are two orbits of corners and when we think about the total number of position we tend to hold one of the orbits of corners fixed. The choice of which orbit is arbitrary but on a physical Skewb one orbit is physically attached to the core. If you want to maintain a symmetry between these two orbits you need the others ones connected to a core too. But that would collide with the existing core. So you can put the new on the outside. I think this is the sort of thought process that Carl went through to develop this puzzle idea .

Brandon Enright wrote: Andreas and Carl, especially Carl have alien thought processes .

That is a blatant lie.

And the fact that he parks his spaceship using a similar handle mechanism is just a coincidence!




Pantazis