# Hexaflexagons

A "flexagon" is a way of folding and rejoining paper to make a flat object which appears to have more than two sides. It can only show two of those sides at once, so you "flex" it - folding it and unfolding it in a particular way - to switch out which two sides appear at a time.

The word "flexagon" was coined by one of four people, all of whom were graduate students in physics or mathematics at Princeton in 1939. They were Arthur Stone, who apparently discovered the hexagonal format you're going to see in this demo; Bryant Tuckerman, Richard Feynman, and John Tukey. All four of them achieved some fame in their respective fields and one of them achieved a fair amount of fame, period. These four did all the initial "research" into the flexagon (read: they farted around with them a lot when they should have been studying.) You can find the whole story, and a lot more detail than this demo goes into, in Martin Gardner's The Scientific American Book of Mathematical Puzzles and Diversions (Simon and Schuster, 1959) - if you can manage to find a copy.

We're going to make two hexaflexagons (the hexa- just refers to the shape of the finished object; there are other kinds). We'll start with the simpler three-sided "trihexaflexagon," because it is easy and shows the basic principles; then we'll try for the six-sided "hexahexaflexagon."

You will need:

- a roll of adding machine paper (not thermal paper)

- a means of measuring a sixty-degree angle

- something to cut the paper with

- something to glue two surfaces of paper together with that will only glue those surfaces (e.g. won't seep through and glue anything else in a stack of layers); I used double-sided tape because 1) I had some and 2) you don't have to wait for that to dry.

Begin by cutting off the end of the tape at a sixty-degree angle. Discard the scrap end or use it as a bookmark.
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mingraham2 years ago
I don't have adding machine paper just printer paper so how wide should it be? a different one that i totally botched said it should be 3.6 cm
EccentricFlower (author)  mingraham2 years ago
Any width strip of paper is fine, as long as you mark it off in equilateral triangles. If you start with a wider strip of paper, you'll just get a bigger flexagon, so no big deal.
vincent75202 years ago
This was a fad among children at school in the late 50' and early 60's in France.
We played with them all the time at intermission between two classes.
If I remember well we also had a guess game that came along : the holder asked how many times he should open and close his folded paper and which color should be revealed !â¦
Didn't even remember that game before seeing this instructable : thank you !â¦
sherrycayheyhey2 years ago
I think I just found my weekend paper project. Awesome!
audreyobscura2 years ago
I just learned about Hexaflexagons! SO COOOL! Thanks for the share.

Kiteman2 years ago
Oh, I had a copy of that book - I must still have, since I don't recall ever throwing it out (have you read the story of the tie?).

Flexagons are very cool, wonderful occupiers of fingers.
EccentricFlower (author)  Kiteman2 years ago
I have indeed read the story of the tie!

Hang onto that book if you've still got it. It (and its sequel, which is just as good) are often hard to find these days.