Hello Puzzlers,

Today I am happy to introduce my latest puzzle, the Twisted-8, now available in my Shapeways shop:

Twisted-8 is a tetragonal trapezohedron with ten axes of rotation. Two axes are at the four-sided vertices, and the remaining eight axes are centered on the edges located around the equator of the puzzle. Here is Twisted-8 after a vertex turn:
And here is Twisted-8 after an edge turn:
Twisted-8 is also capable of shape-shifting (I'll leave it to the experts as to whether it qualifies as jumbling). To do so a vertex is turned 45 degrees rather than 90, as shown here: Edge turns can then be made, resulting in shape-shifts as shown here:

Twisted-8 was designed in Solidworks, and made in Shapeways BSF material.

Here is a video.

I hope you enjoy!
Dave

This is really great, an instant favorite for me! I love the symmetry on this puzzle and you did a fantastic job. Is it possible that this will be available through Shapeways? I would love to see this beast's mechanism!

Chris Hemerich

Wow! I love how your puzzles discover and utilize strange new symmetries. I don't think anything like this has ever been done before!

It almost reminds me of Timur's puzzles, but that's probably just the strange geometry, and the stars.

What he said

Really, I just love these crazy symmetries. It doesn't seem like the mechanism would be horribly complex, but I can imagine that it is.

Wow! another fantastic puzzle. Keep up the good work!

WOW!!! What an interesting geometry. Is there a shape mod of this puzzle that doesn't change shape after that 45 degree turn? Well I guess you could say a sphere... So let me ask it this way... If this were a sphere would this look unchanged after one of those 45 degree turns if the stickers were left off? I'm not sure but I think the answer is no. If I'm correct then I'd say this puzzle jumbles. Another way to tell, check if some of those edge turns are blocked after the 45 degree vertex turn. I can't really tell from the pics but I believe some of them should be blocked if this is a jumbling turn.

And looking at this geometry some more it looks like a puzzle with this appearance could have even more turns.

It looks like you could have vertex turns along the red cut. If so that would probably be a jumbling turn as well as that is an isosceles triangle. And you may even be able to have what I think may be a deep cut along the green cut. Looking closer, I'm just not sure, if either of these cuts were present would they allow anything but 360 degree turns? If that is the case then they'd add nothing to the puzzle.

Carl

Amazing!! I like it. You are a genius.

Masterpiese Puzzle!!!

You are really good at this! You just came out of the blue and gave us 3 amazing puzzles! Have you been browsing the forum for a while? What program do you use?

-Eitan

Hi Dave,

That is a fantastic design, again and again!

Could you help me understand the geometry of the puzzle? Suppose that you would shape-mode this puzzle into a face-turning puzzle, with all faces at the same distance to the origin, what would it then look like? A face-turning square anti-prism perhaps?

When developing AntiCube, I discovered that the corners would have almost a five-fold rotation symmetry. I tried to fudge it into true five-fold symmetry, but failed. That is why I eliminated the corners at all,leaving only a set of fudged edges that can all be interchanged. Looking at your puzzle, I think it jumbles, but there may be no fudging and your pentagons do not have exact five-fold symmetry. Correct?

Oskar

Like a face turning octagonal prism?
Fantastic designs you've got!

Can you sell this on shapeways please?

It's definitely one of my favorite, and quite smooth considering the edges are deep cut as much as on a starminx II

Beautiful. Very interesting properties. I seriously have no idea how you come up with all these ideas. And I agree with others, please put it on Shapeways!

Woooow! Each of your puzzles is more mind-blowing than the last.

I love the colour combinations too.. Purple orange yellow / maroon green orange ..Very unusual, spectacular all round.

Cheers,
Burgo.

Keep them coming! You've released some pretty amazing puzzles already!

Thanks for all the great feedback and excellent questions! Sorry to take so long to reply, but I'll try to answer all the questions here.

Regarding selling the puzzles, I do plan on making Twisted-8, Ice-9, and Fracture-10 (and possibly others) available on Shapeways. However, I won't release them until I am fully satisfied with the function of the puzzles. In the case of Twisted-8, it needs a few changes to work as smoothly as I'd like. Hopefully within a month or two I'll have a shop open.

Thanks for the compliment! I actually have been on the forum for quite some time, and have been designing puzzles for many years. Back when this site was the Twisty Megasite, I helped Wayne prototype parts for his 6x6x6 design, created (what I think was) the first fully functional 3x3x5, and the first working design for a face-turning octahedron, among other things. But since intellectual property theft is rampant in the industries I have worked in, I have always been very reluctant to reveal my work publicly. But I have finally come to the realization that it is better to show my creations here than to never have them see the light of day. Now on to the puzzle itself...


For the turns shown in red to be possible, the puzzle would need to be a pentagonal trapezohedron, as shown here: In this case, the puzzle becomes a vertex-turning starminx, combined with two horizontal starminx II slices. The slices highlighted in green actually do not line up, even though they appear to from some viewing angles.
Here is a picture of what the puzzle would look like shape-modded as described: The slices on the vertical sides are at the edges of the prism faces. All of the equatorial axes of the puzzle are in the same plane, so no anti-prism angular changes are needed. You are correct in that the pentagonal faces do not have five-fold symmetry (shifting to the pentagonal trapezohedron would be required), and there is no fudging involved in the design. I think for this to be a true jumbling puzzle, you would need to be able to turn the edges 90 degrees, and then make further turns. This is possible with the locations of the horizontal slices on the octagonal prism shown above, but to work with the trapezohedron geometry the shape must be stretched significantly, as shown here: Here is the same shape with a 90 degree edge turn: As you can see, the slices would now align to allow vertex turns, and some edge turns. Other edge turns would be blocked, creating my understanding of a "true" jumble puzzle.

Here are a couple more pictures, first of the puzzle scrambled without shape-shifting, and then of a shape-shifted scramble:
Hopefully that answers everything, but let me know if you have more questions.

Dave

Holy cow! Dave, I must bow before a master. I joined the forum about 2.5 years ago, and I haven't had a chance to dig around in the really old posts, but it sounds like you were one of the original founders. I'm really glad you decided to post again, as these puzzles rock!

-Eitan

You are right with with your guess in the question. This is indeed a shape transformation of a faceturning octagonal prism. Look again at the image with the scrambled puzzle: The pieces at the equator did not change their shape or position. These pieces are the transformed faces of the octagonal prism.
Therefore: no fudging (so far so well known) and no jumbling.

And:
I want to second Hugo's second line. (What a line )
Very clever puzzle.

THANKS!!! These are all GREAT puzzles and I'm happy you'll be making them available. I understand your concerns about intellectual property theft but I'm so happy you have allowed these puzzles to be shown. It's actually hard to believe some of these ideas are as old as they are and they are still so original.

Thanks. That makes it VERY clear this is a Shape Mod. See the definitions here.
There is no fudging or jumbling in the Twisted-8 as presented.

Actually I really like that Face Turn Octagonal Prism too. You should offer that in your future Shapeways shop too.


Yes, are are correct. THAT would be a jumbling move. And I think I prefer the Face Turn Octagonal Prism over the stretched trapezohedron... but that is just me. Both would make GREAT new puzzles.

Carl

Thanks for the compliment Eitan, but I had nothing at all to do with establishing the site. I really stayed "in the shadows" back then, and did not post any of my early puzzle designs until recently. I may have been making puzzles for a long time, but if I am a master, then you and many other of the extraordinarily talented designers on this forum certainly qualify for that title as well.

Here is a modified octagonal prism that would make a better puzzle since the vertical faces are divided:

I realized that I was wrong about the shape needing to be a pentagonal trapezohedron for the minor vertexes to allow turns. These turns could be made possible (as Carl suggested above) by stretching the tetragonal trapezohedron slightly, as shown in the first image below. However, if both edge and vertex turns were allowed, many moves would quickly become blocked (unlike the pentagonal trapezohedron). The second image is the same shape, but exclusively vertex turning, creating something akin to a "dino" trapezohedron. The third image is a combo edge & vertex design with some "unbandaging" slices added.
So I have two questions: First, any thoughts on which variant (if any) would make for an interesting puzzle? Second, does anyone know how to figure out how many "unbandaging" slices would be required to allow a combo edge/vertex turning version to be mixed thoroughly?

The 2nd one is good enough.
The 3rd one is too difficult to solve. And the unbandaging slices will be too compicated.

The other easier variant:

Personally I find them all very interesting.

I'm tempted to say none. Just don't turn the 3 sided vertices much. Limit most of the turns to the edges and the 4 sides vertices and I believe you should be able to mix it thoroughly.

Carl