What The Heck Is A Hexaflexagon?

Recently, fidget toys have become extremely popular. Fidget Spinners, fidget cubes, and many other kinds of toys are being heavily marketed to children, but they are not the first kind of distraction ever. A older kind of fidget toy is something called a hexaflexagon, a hexagonal toy that can be folded and played with. They are most often made with paper and tape or glue, and can be decorated and colored however one may like.

When Were They Created?

In 1939, at Princeton, Arthur Stone was playing around with strips of paper that he had cut from around the edge of his binder. He had folded a slip of paper like an accordion in the shape of a triangle. Taking these equilateral triangles, he folded them in the shape of a hexagon, then taped it together. He was just playing around with his hexagon, when he pinched the sides to create the inverse of a triangle, when the inside popped out. Repeating the motion, he found that he could do this indefinitely.

Stone decided to bring his flexible hexagon (flexagon) to the attention of his friends, Richard P. Feynman, Bryant Tuckerman, and John Tukey. This group of four dubbed themselves the Flexagon Comittee, and while together, they discovered ways to make flexagons with many different faces- up to 48! Feynman created a diagram, called a Feynman diagram, which displayed every way to change the color you see on a flexagon, or to flex it to another side.

Unfortunately, as World War Two began, flexagons were forgotten, until 1956. In that year, Martin Gardner was

visiting a friend, when his friend showed him a flexagon. It was made of cloth, and Martin Gardner was immediately amazed. He did research then wrote an article for Scientific American, which brought back them trend. In 2012, Youtuber and Khan Academy educator in math, ViHart, created a string of three videos about hexaflexagons. Since then, in mathematical communities and schools alike, hexaflexagons have become slightly popular, but not nearly as popular as fidget spinners or cubes.

Are They Easy To Make?

Yes! All you need is paper and tape/glue. Here’s how to make a basic, 3 sided hexaflexagon.

    1. Cut a paper strip. White paper is thicker than notebook paper, and is much easier to color, too! Try your hardest to make it as even in width as possible.
    2. Using that paper strip, fold it up into little triangles. There are two main methods to do this:
      1. You can either put a small dot slightly past the edge of the paper by approximately 1 centimeter. Fold
        in at that dot, making it the vertex. Then, using the edge that you have folded as a guide, fold your paper into triangles.
      2. Take your paper in the middle, and fold one crease until you get a shape that looks like a V. Fold the back-most edge backwards again, so that the new crease goes along the edge of you paper strip. If when you do this, your triangle covers only part of the strip, push it until you cannot see anything beneath the triangle.
    3. Continue step 2 until you have no other paper to fold, creating triangles on both tails of the paper.
    4. Take your new paper strips and allow them to fold as they would like. They should naturally want to form a hexagonal shape. There should be three dividing portions that are evenly spaced. If your hexagon has one side that has 3 triangles with no separation, try folding them again, until you have a hexagon made of 3 sets of two triangles in the shape of a diamond. Cut off the tail so you only have one triangle on the edge (pictured right).
    5. Once you have the hexagon shape formed, decide on your method of connection, either glue or tape.

 

      1. TAPE: Cut off the triangle which is colored red. Tape the edge where the red triangle is to b
        ond the two sides.
      2. GLUE: Press the triangle coloured red on the right to the triangle colored green on the right, then glue. Press together and hold until the glue dries, or for a few minutes.

 

  1. Color, and enjoy!

Ok, I Have It Made. Now, How Do I Press It?

Here is a handy dandy gif to instruct you, because it is incredibly difficult and mundane to describe.

 

via GIPHY (By me)

 

Why Did I Not Know About This!?

I know, right! Such an awesome invention, such little appreciation. Fidget Spinners, which have only been popular for about half a year, are way more popular than flexagons have ever been. Flexagons, which have been around for decades, have barely been popular, despite the fact that they cost less than a dime, but spinners,

which have only become popular in the last year, and regularly cost above 5 dollars, have skyrocketed to popularity. I conducted my own poll with 20 kids in my journalism class, in which I asked three questions:

  1. Have you ever heard of a hexaflexagon?
  2. Have you ever used a hexaflexagon?
  3. Have you ever used a spinner?

I put the results into a chart and the results are crazy. Almost no one in my class had heard, of, much less used, a hexaflexagon, and nearly everyone had used a fidget spinner.

So what are you waiting for! Spread the flexagon love!

Sources:

https://1000hexaflexagons.weebly.com/explore.html

vihart.com

youtube.com/user/vihart

giphy.com

docs.google.com/spreadsheets