DodecaHexaflexagon


A couple days after making the flexagons, I got the urge to try something a bit more complex. So, I went to flexagon.net, to check out their other patterns, but it seems that I’d already downloaded the better looking ones. The harder ones were just templates, with no artwork. The only remaining choice was the Zodiac-styled 12-sided DodecaHexaflexagon. However, that required 8 sheets of paper, and I wasn’t sure if I wanted to use up that much ink, given how expensive ink is. Eventually, though, I broke down, printed the pages out, and spent a couple hours gluing the sheets together. There are 4 different ways to fold this beast, and I settled on the standard, simple pattern shown above. Unfortunately, the way this pattern is designed, it’s really easy to mess up gluing the last tab in place. The paper has to be folded into a tight little pocket, and the glue adhered too high up along the edge of the pocket. Trying to pull the tab loose to reset it just made the paper rip up.

I seriously considered throwing the whole thing away, but I realized that I could cut the torn tab off, print a new sheet containing that tab and the next adjacent triangle, and glue on a new tab to try again.


(Unfolded, the strip is about 4 feet long.)

So, that’s what I did. Then I tried a different folding that would bring the glue tab points out where I could get to them more easily, and they wouldn’t form a pocket. That didn’t work out because the pattern, when fully folded up, is 16 sheets thick, and the stresses on the fold lines caused them to start tearing from the outer corners. I finally gave up, went back to the original pattern folds, and just squeezed the pocket open larger to make it easier to get the tab into place. Even then, the tab kept curling up and touching the inside of the pocket in the wrong spot. My next hope was that no one would notice.

Folded back up, and with the glue tab more or less in the right location, this flexagon is about 5-6 inches at its widest.

There are 12 individual sets of faces that can be exposed by turning the ring inside out, but each folding only reveals three of them. The only option is to cut the ring again, glue on another replacement tab piece, and go to another folding. If there was a way to hold the tabs together with a paperclip, that would be ok. But again, the thickness of the finished flexagon puts huge stresses on the paper at the fold points, and tearing is a problem.

At least for the moment, the face with the messed up Pisces tab isn’t obvious. I’m not likely to make any more of these in the next few months, anyway.

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