15-30 min
In Progress
Lesson 1 of 0
In Progress

Flexagon

15-30 min

Intermediate

Ages 8+

What Will You Learn?

Invented by Arthur H. Stone in 1939, flexagons are mathematical, multilayered objects composed of folded paper strips. They usually take the form of a square or hexagon, and there are several variations on the type of flexing and number of faces. When a flexagon is flexed, a new face is revealed. Flexing is similar to folding, but it’s not a static motion where there is a beginning and ending point; it’s a fluid and continuous forward and backward motion. For our project, we’re going to create a standard square flexagon, known as a tetraflexagon, which will reveal 2 new faces.

To Make your Flexagon

Step 1

First, cut out both of the L-shaped strips on the second page of the PDF. Note that they’re double-sided.

Step 2

Next, lay them horizontally, so that the tallest side is on your left. (The text on side B-1 will be upside down.)

Step 3

Starting from the left, fold over to the right. Repeat.

Repeat Step 3 with the second strip.

To Flex Your Flexagon

Step 4

Remember that this is a fluid, rotating motion.

Begin with face 1 (pink) facing you.

Step 5

Push both the right and left sides downward.The profile should look like a mountain peak.

Step 6

The first new face, face 2 (blue), will be revealed from the center of the flexagon; with your thumbs, open it up like a book.

Step 7

Repeat Step 2 to reveal face 3 (yellow, second new face).

Step 8

Return to face 1 by reversing the fluid movement. You will be flexing the outside edges toward the center. The profile should look like a V-shape.

NOTE: A second method of returning to the starting point is by flipping the flexagon over so that face 4 is facing you and flexing it twice. Then flip it over once more and face 1 will be facing you.

What's Next?

Try out other shapes

Try other Flexagon shapes!

https://makezine.com/2009/02/15/make-a-flexagon/

Maker Numberphile’s Forgotten Flexagon

https://youtu.be/7H4lDi79YY8

Try Vi Hart’s Hexaflexagon

https://youtu.be/Svq2Kscmmwc

Books to read:

  • The Magic of Flexagons: Paper Curiosities to Cut Out & Make by David Mitchell

  • Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games by Martin Gardner

  • Flexagons Inside Out by Les Pook

About the Magazine

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Maker Camp is a do-it-yourself online resource to help leaders like you organize a summer camp that engages children in making. Our goal is to provide you and your campers with the inspiration and the helpful resources, along with many possible projects to fit a wide range of interests and abilities. The idea is to focus on making as a playful, social activity. Maker Camp provides enough support for anyone to get started. Making provides experiences that help children become self-directed learners and good problem-solvers.
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