Flexagon, Folding Paper Machines
This is my flexagon. It is a tetra-tetra flexagon. Or has four faces and four sides. By folding, and sometimes pinching and flexing, these little paper devices you can check change numbers or colors or patterns. Numbers or colors or patterns well up from seemingly flat dimensions in an (almost) never ending succession like a mobius-strip come alive! Although instead of creating a 3D shape from a flat piece of paper and then making it 1D this mobius-strip "snake", the flexagon takes a flat piece of paper and cycles of into the realm of 3D momentarily and then end with a 1D/2D changed first world.
Each flex, pinch, fold or flip can change the image, pattern or number by a little or a lot. Flip, meow, flip!
In 1939 Arthur Stone, Bryant Tuckerman, Richard Feynman and John Tukey published a paper of their mathematical findings after Arthur Stone discovered the hexa-flexagon. Flexagons can have as few as three sides up to an infinite number: whatever your brain can come up with, provided you have a big enough piece of paper.
Here is my humble collection of flexagons. There are various shapes, which necessitate different maneuvers-not just flipping like the first video.
Pinch, flex, pinch, flex...
This last hexa-hexa-flexagon has six sides and six faces, so many in fact that I stopped flexing it at just the 5th face/side...I just got lost between dimensions and couldn't find the sixth.
I'm stuck in dimensions too-meow!
Jacob's Ladder Toy
Something very similar to a paper flexagon is this Jacob's Ladder Toy I made from some La Florentine candy boxes that my boss gave me.
There are tons of great instructions online on how to make these. My two tips: don't make the ribbon attachments too tight; and use heavy boxes. I ate the candy, so my boxes are too light and don't flip as fast as they could.
Although it's "automatic" and quite impressive looking in action, the Jacob's Ladder Toy is much less sophisticated than a flexagon. Add we've seen previously, a flexagon can have many phases it can cycle through. My Jacob's Ladder Toy can only flip the boxes upside down or right-side-up.
I'll probably throw some pennies into the boxes to weight them better.
