What is a flexagon, you ask? At first glance it looks innocuous enough, like a folded hexagon or square, a child’s fortune teller or cootie catcher, or a piece of origami. But look closely and you’ll see hidden layers lurking between the front and back. When you fold or pinch corners together, the flexagon “flexes,” meaning a formerly hidden layer will come to light as the top layer folds underneath. It all sounds complicated but is really pretty simple when you see an actual flexagon in action.
Mathematicians refer to flexagons as “mathematical oddities.” That’s because flexagons have very complex mathematical structures. As the flexagon is flexed, sections shift position to create an almost kaleidoscopic effect, and different faces come into view, in cyclic order. Mathematicians enjoy analyzing the structure and dynamic behavior of flexagons. Laypeople just enjoy playing with them.
Flexagons can be made in several shapes and sizes, with complicated names like “trihexaflexagon” or “heptahexaflexagon”. Below are the instructions for a simple flexagon that you can make with your girls.
- One piece of 8.5×11” paper
- Fold the paper so that the long edge is in quarters and the short edge is in thirds (as shown)
- Number the squares as shown.
- Flip the paper over and number the back as shown.
- With the front side showing, cut along the dotted line.
- Fold the “door” back behind the far left 3.
- Fold the 3 on the left side on top of the other 3 so you get a vertical line of 1s.
- Then fold the right hand side back between the 2s and 3s and then fold again between the 1s and 2s so you should get six 1s showing.
- Stick a piece of tape between the two middle 1s (make sure it is only on the middle squares!) On the back should be the 2s. Fold this back to get the 3s. Fold it again to get the 4s.
Image and instruction source: http://www.mathemagic.org/MathsAndArt/flexagon.htm