Flexagon
15-30 min
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
Try Vi Hart’s Hexaflexagon
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
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