Trying to sync to facebook again
We’ll see if this works.
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Seems to have worked.
I sync it did.
Heh! Now let’s see if these comments get pulled back to WordPress this evening. (It happens once a day.)
I don’t post on my blog that often, but there are about four or five posts that haven’t sync’ed.
And what’s the basin for your comment…finding it a bit draining? LOL
Hi Kathryn. I apologize if I’m “out of sync” by asking something outside the subject matter for your current post. I loved your flexagon page. I was hooked on flexagons about a year ago, and have succeeded in building them up to 6 faces. You mention on your hexahexaflexagon page it is possible to come up with 12 faces by making a longer strip of triangles. Then the instructions are “repeat the folding for figure 2 until you’ve reduced the strip to the length of figure 2.”
Could you write me an e-mail, or post on that page, more details about how to fold together a 12 faced flexagon? I’ve ruined strip after strip trying to figure it out on my own.
Sadly, I’m not a mathy person or a techy person. I’m just a grandma who loves to make paper toys. I would be so grateful if you’d give me some directions so I can put together a 12 faced flexagon.
I have 6 faced flexagons everywhere. Some I draw designs on then pass along to kids. But for the most part I like to use them to memorize things like long numbers or poems or verses or in learning Spanish.
Thank you!
Carol
No problem. Let me think a bit and I’ll either send you something or add an example to my page.
I regularly make 12-sided flexagons. It’s my favorite size.
I should add that I went through my flexagon drawer and found a 24-sided hexaflexagon that I made, probably about ten or twelve years ago. It’s difficult to flex, because there are so many layers, but it can be done.
Making either a 12- or 24-sided hexaflexagon is basically a matter of doubling or quadrupling the number of triangles from those for the hexahexaflexagon and folding as in step 2 of the instructions in the previous link.
That’s really all there is to it.
I should say that you are performing step 2 twice, thus halving the effective number of triangles so that the basic shape resembles that for the hexahexaflexagon.
Hello again. Maybe my problem is in numbering. I’ve got the strip made and the numbering starts out as thus: /0b\2c/1b\oa/2b\1a/0b\2a/1de/2d\1e/0f\2e/1fc/2f\1c/0b\?/0b\2c/1b\oa/2b\1a/0b\2a/1de/2d\1e/0f\2e/1fc/2f\1c/0b\
At the inverted triangle with the question mark, should I start the renumbering at the question mark with 0b, or leave it blank, or do it in another way? Same as with the back side, I’m not sure how to do the numbering.
Thanks! I’m soooo looking forward to getting this right. Even though I’m not mathmatical in any way, shape or form, I really do love these flexagons. To me, they are just magical.
Carol
I can’t remember. I could take one apart, I suppose.
You could make one without labels, label it, then take it apart again. That’s how I initially figured it out.
I can’t locate the program I used to generate it. It might be on the backup from my last Windows computer. I actually haven’t made one in about five years. That’s when I switched to the Macintosh.
Got it! After many trials and errors and tears and groans and moans, I figured out how to fold up the 12 faced flexagon. Funny I can’t find that 12th face – only 11. And my flexagon is quite clunky looking. But the important thing is I did it.
Now that it’s done, I guess I like the looks of the 6 faced flexagons I’ve made, as they don’t look so mangled. It’s really quite tricky, isn’t it? I guess I can see why no one has put up exact instructions for it. A 12 faced might not be that popular.
I’ve made a number of 6-faced flexagons with tyvek paper. A flexagon made with that stuff is nearly indestructible. But since I don’t have long strips to work with, like the adding machine paper, the flexagons are small. I’ve just been buying the legal-sized tyvek envelopes and cutting them apart. It makes great flexagons for children’s gifts as they are hard for little hands to destroy tear.
So thanks for your help with this, Kathryn. I appreciate your communication with me. As I read your blog, your posts and people’s comments, I see that I am so out of my league. I’m not quite in the class of a Beverly Hillbilly but you might think so. I certainly don’t have Granny’s money!
Thanks again.
Carol
Oh, I don’t judge anyone. Something I got from my father, may he rest in peace.
My 12-faced flexagons are pretty reasonable. They flex fine. I use legal paper for an inkjet, and make two strips from a sheet. I glue those together to make one long strip.
I had never thought of using Tyvek! That’s a great idea! How does it crease?
Tyvek creases just fine if you score the lines first.
Something else nice about Tyvek is you can use markers to color the triangles or number them and it doesn’t bleed through.
Have you ever made puzzles with flexagons? I got the idea one day from some web page, and started drawing a line that you have to follow (basically using the Tuckerman Traverse). Another fun idea, as a gift for a special child, is to make a rather large flexagon with heavy paper or card stock, and then tape a five dollar bill that’s been folded into a triangle into one of the harder faces to find. I’ve done a number of “treasure hunts” with them, give instructions on the first face to “find the flower” or whatever picture it is that I put on the hardest to find face. Another “seek and find” game is to punch a few holes on one triangle, the back side of it being part of a hard-to-find face with lots of color that shows through the holes.
The possibilities to have fun with flexagons are endless. It’s so fun being a grandparent. And these games are so easy to send in the mail. Even the largest flexagons fit in the envelope because you just fold them in half.
Have you ever tried making a 6 faced flexagon with something other than paper — say, thin pieces of wood? I saw a sample of one on the internet, some fellow who makes coffee coasters out of them.
Carol
I can see that, since Tyvek is waterproof. I’m going to have to try that.
I’ve generally used a Java program that I wrote back in 1996 and can’t find right now to import face images that I create in a graphics program and lay out the triangles into the strips. Then I print the result on an inkjet printer. The problem is that inkjet ink is water soluble, so my older flexagons have little water marks on them. (Or cat teeth marks.)
I don’t have a steady hand, so I don’t trust myself to draw on them, though I did that to figure out how to lay out the faces.
Ooh, I like the puzzle idea! You wouldn’t want to have more than six sides for that, though.
Martin Gardner had an example in his Scientific American article (from 1957?) of coloring symmetric designs and making snowflake patterns that change as you flex. I have thought about using them as Christmas cards, which just three sides to make it easy.
I have never used anything but paper. I thought about trying a 24-sided one again using fabric and stiffening the triangles with Stitch Witchery or some such, leaving some untreated fabric for the folds. (I like ceramic for coffee coasters.)
Apparently, I’m more conservative in my flexagon fabrication than I had thought…
This is a fun conversation!
Something new! Cut out a plain flat hexagon about the size of a six faced flexagon, well, just slightly smaller. Write a message on it, print a picture on it, a puzzle, a joke, etc. then fold it up into a triangle shape. Glue the bottom triangle into the triangle of one of the flexagons. It works best to use the face where three of the triangles have just the one layer of paper. I’ve been trying to figure out all weekend how to fold a dollar bill into an equilateral triangle for a fun surprise to open up to. So far I haven’t liked my results.
Haven’t tried it, but I suppose a folded hexagon could be put on every face of the flexagon except for the first and bottom of the first, so a child or birthday person or whomever could follow some kind of special message, like a treasure hunt. I just don’t know how thick it would make the flexagon. But one folded up hexagon works just fine.
Hmmmm… I should try to get creative here… maybe something like an opening flower or some other folding thing could be incorporated into one of the faces. Actually, a trihexaflexagon on card stock would work well for something like this, just to have the person open up to something pretty or unusual or clever.
I’ve been experimenting with a 6 faced square flexagon on card stock paper. I found directions online to cut one out of a folded square, just cutting out the center but with no other cuts. I’d love to find one with a dozen faces, but I haven’t found a pattern. I found one with more than six faces, but the directions were very vague at how to fold the thing up.
Happy flexing! Hope you are having a great week. My dad turns 84 today. Quite a milestone in his life, considering his health.
Carol