Septic Twist combines several ideas. Bram Cohen asked Oskar: "can you design a twisty puzzle with septagons?". Andreas Nortmann asked Oskar: "can you build a puzzle reusing this mechanism by Wayne Johnson?". The result is this puzzle with four heptagonal centers and 23 edges. The puzzle is not too hard to solve, but it looks quite nice.

Watch the YouTube video.
But the puzzle at my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar

This reminds me of Timur's Skyglobe.
Nice realization of the given challenge.

Cool! Looking only at these pictures, one might think that there's a trick, because it's just not possible to make such a symmetrical shape. But there's a symmetry-breaking "wrong place" that flickers a couple of times on your video. Are you intentionally hiding it?

You can see that "wrong place" on 1:20 of video.

Nice puzzle. Not to sure I like the name. There is more then one meaning to Septic.

Carl

Carl,

If you get ill from this septic (infection-causing) puzzle, then I suggest you switch to the Anti-Virus puzzle.

Oskar

There it is! Very nice.

Can you post an image showing the "backward region" which allows the puzzle to work?

Now it is time for another theory-session:
Is the puzzle fudged?
Are there some stored cuts in the "backward region"?

Added.No.No.

Andreas, thank you for taking such good care of the TP Museum, by the way!

Oskar

I forgot to ask this question: Do the axis of the four layers meet in one point? And thank you for uploading edited images. This saves much of my time! In these cases I add all images.There are stored cuts. The gap marked by the red line can't be used directly. You have to make another turn before you can cut through this gap or have I missed something?

Yes.You are right.

Oskar

Just catching up on the thread and I was about to ask this same question. Nice to see its already been answers. So I'll ask another one. Look at this pic.

I notice not all the edges are unique. So does this puzzle have a unique solved state? Edges 1 and 2 look identical but I'm not sure you can get edge 1 into edge 2's position without flipping it.

Looking at edges 3 and 4 its easy to see you can get edge 4 into edge 3's position and no flip is needed but can you swap edges 3 and 4 at the same time?

Curious,
Carl

This is irrelevant to this puzzle but it is another challenge. Oskar, have you ever tried to design a puzzle with non-circular gears?

Well, it could have been worse. The name of the puzzle could have been Septic Tank!

Oskar, you never cease to amaze me...

GAP tells us:
This puzzle has 4067864883367957555618775040000 permutations and there are 32 different solved states which can't be distinguished.

Just realized you don't need to go to the "backward region" to find stored cuts. Here is another example:

Interesting. 32 is 2^5 so one might expect 5 pairs of identical edges which can be swapped. However I see 6 pairs of identical edges if I'm looking at things correctly. I see 4 pairs similiar to those I've numbers 3&4 above and I see 2 pairs similiar to those I've numbers 1&2 above. I believe this means the 3&4 pairs can be swapped independantly and the 1&2 pairs can only be swapped if they are swapped together. Without holding the puzzle in my hands I'm still not seeing how one can flip those edges but I believe this tells me it is possible.

Thanks,
Carl

Hey Carl, I think only an ever number of swaps are possible. The complicated geometry of this puzzle makes it hard to look at and really see all of what is going on but 7-cycles are even permutations.

I think the 32 actually arises from the number of ways you can choose an even number of swaps from 6 pairs:

? ncr(n,r) = (n!) / ((n-r)! * r!)
? ncr(6,0) + ncr(6,2) + ncr(6,4) + ncr(6,6)
%1 = 32

I do see how to flip one type of edge. I'm not sure if all edges are the same or not though.

Thanks. Yes, this makes more sense then my first theory. And looking at the front of the puzzle I too see how an edge can be flipped with 3 turns. And I'm pretty sure all the edges are identical from a mechanical point of view. Looks like each edge can get in any position in any orientation.

Looking at one of the puzzles which inspired this one, the Wayne Johnson's Jewel45. I can see how this is somewhat related to the Mixup Cube. The Mixup Cube allows 45 degree turns on the slice layer but only 90 degree turns of the face layers before the puzzle returns to a doctrinaire position. The Jewel45 is the inverse of that. It has 45 degree face turns but only 90 degree slice turns. You could also say the Mixup Cube makes the face centers and edges the same piece type. The Jewel45 does something similiar with the corners and edges. Each corner is cut into 3 pieces and those are now the same type of pieces as the edge pieces. Looking at the Jewel45 in that light makes it a bit easier for me to see what is going on here.

Thanks,
Carl

If the group of the Sepctic Twist is restricted to edge flips only the groups has 2^22 elements.

There are three faces meeting together, so edge flips should definitely be possible.

Maybe my statement was too cryptic. With different words:
There is no way to flip a single edge and leave everything else as it is.