A Flexagon Initiation

A flex-uh whut?! Heheh! welcome to a new toy that knows no age! While I was cleaning up taxes earlier this month, I was distracted by following a couple of links on U-tube to a folded paper creation called a flexagon. I have a weakness for folded paper thingies and found myself sucked glassy-eyed toward this new attraction like a moth to the flame. However, priorities prevailed at that moment and I bookmarked sites for later exploration. Today I had slotted a couple of hours for playtime and all too easily gave up much more after downloading a basic software for creating a flexagon with my own images. And I’m going to share this new little addiction without any apology!

First, a smidgen of history for those who like to know everything about a new thingy (I had to find out!), although this devious paper contraption has been around for some time, messing with minds of all ages. Although I imagine that this construction has been discovered by many and likely several times over, the established story is that in 1939 a graduate student in England, Arthur Stone, trimmed his American paper to fit his English binder. Keenly sharp in mathematics, he began doodling and folding these scrap paper strips, forming a “flexible hexagon”, or, as it was soon named, the “flexagon”. Evidently he quite happily spread the infection of this mysterious paper invention that could flex to expose faces previously hidden. Historically much of the investigations into addictive variations … caution: there are MANY! … revolved within the circles of mathematically bent adults for several decades until it broke out and into the hands of the young and restless.

Relax, I’m going to woo your interest with the classic flexagon, and this is a hexaflexagon also known as a tri-hexaflexagon because of the three faces and hexagonal shape. While I’m playing with creating a line framework in my draw software (yep, I have it that bad!), here are two flexagons generated with a free plug-in software I found in my online research. If you’d like to mess with this yourself … it’s surprisingly easy if you have a decent photo software … here’s the url and instructions for use: Foto-TriHexaFlexagon. I would recommend printing the whole website page for reference while setting up this simple software for the first time. Or you can simply play with ones I’m giving you!

Below is the very first flexagon piece I eagerly generated, a “what if I try” of photos of spring flowers from my garden … bright Dutch iris and alyssum. Follow the images and you’ll quickly be flexing your own flexagon. Click on the image below for the largest possible image … right click to copy and paste into your photo software to save and print. I would recommend printing on legal size paper if you can (I use 24lb), to maximize size for better folding and flexing. You can go into your printer’s Properties to select Legal and Landscape orientation to successfully print the image … for most printers you can also adjust the size percentage if necessary up to 13 inches in width for maximum size. This creates a completed flexagon of about 4 inches across.


After cutting the image from the background paper, fold the strip of triangles in half along the long horizontal middle line carefully aligning the open edges. Use a glue stick on the smaller side, folding and smoothing to keep it flat as it dries. Gluing the sides together will leave two white triangles exposed at each end, soon to be the connecting tabs to the completed flexagon. Allowing time for the glue to dry, pre-crease firmly along all marked lines and be sure to crease each line in BOTH directions as this will ease the first time flexing through the faces of the flexagon (say that out loud quickly!). The image below shows the glued strip kinked from creased folds.


Make a mountain fold (crease pops upward) along the black line shown above … tucking the left end underneath to match the image below. Notice that the photo triangles are matching across the fold of the left side and top.


Make a valley fold (crease pushes downward) along the black line … folding the right end over to form the shape below.

The photo image matches now with the exception of the last triangle, pinned with my finger. To complete a flexing hexagon, slip the mismatched triangle underneath — below left. Flip the flexagon over and the white ends are now next to each other, one extending outside the hexagonal shape — below right. Take this extended tab and fold it over to meet the other tab, white face to white face. Glue these two areas together, only allowing glue on the white backs; don’t let glue touch other areas or the flexagon will not flex properly. Note to parents and teachers: kids under 9 years are going to need supervision for clean edges, crisp folds and glue in all the right places.


























Allow time to dry — oh, hard to wait! Pick up the hexagon and notice which lines from the center are open layers, not the smooth drawn lines. Pop these layered edges into mountain creases, pushing the hexagon into a tri-fold as shown — above right. These mountain folds will begin to open as the outside edges press downward. The first time these stiff edges are flexed, the tips at the center may need coaxing apart … this is why you did all the pre-creasing! As the center edges flex outward, a new face pops upward — below left. Repeat the same pinch ‘n flex to expose the third side of a two-sided hexagon. Come on, is this cool or what!










Ah, but wait! turn the flexagon over and the reverse side will show a face inverted … namely, what was on the outside corners of an original face is now at the center —below. Technically there are SIX faces; the original three, plus those three in flexed or inverted arrangement. Go on, play with it and find 'em all!

I’m handing off the second flexagon variation below because I couldn’t stop at just one (did I mention these silly things are addictive?). The second flexagon piece features fossil faces; ammonite chambers, suture pattern of an ammonite, and a seastar. This one should appeal to the guys, sons and grandsons, more than the floral variation. It is easy enough for a five year old to play with and charming enough to suck in an adult. And then, AND THEN you’ll start wondering about new combinations ….. maybe even coloring your own doodles ….. hmmm.