Hexaflexagons and Geometric Games to make

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Paper Toys: Flextangles

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Today’s paper toys, Flextangles, are the fourth project in our collaborative series STEAM POWER: Empowering kids to explore the world through creative projects. Today’s topic is COMPUTE!

Since I recently answered this question wrong, I decided it might be good idea for me to limit my math based project to something I’m good at: geometry. I’ve been itching to try making a flexagon ever since my friend Erica mentioned them, so I decided it was high time we made one. If you aren’t familiar with flexagons scroll down to find out more. I also decided to incorporate drawing into the project to add a level of “computation.” Decorating these and then seeing how the patterns and colors translate once folded is a wonderful exercise in geometric planning.

PRINT TEMPLATE HERE

Materials

• Paper, this cardstock works really well
• Template
• Pen
• Markers (I’m nuts for these colors)
• Scissors
• Glue we used this glue because it’s tacky and sets up quickly
• Tape (optional)

• Step One Download and print the template
• Step Two Draw different designs in each row of triangular sides. Refer to the Pattern Guide on our template for the row layout. Be sure to connect the designs at the tick marks.
• Step Three Cut along bold line.
• Step Four Crease dashed lines face to face. Unfold.
• Step Five Crease diagonal lines back to back. Unfold.
• Step Six Gently fold paper to match dot to dot and form a tube.
• Step Seven Add glue on tabs marked GLUE and press together.
• Step Eight Add glue on end tabs and tuck into open end of tube. Press to seal. Let dry.

You’re done! Go play!

Troubleshooting

A few people have written to me to express some challenges with this project. Here are my suggestions for troubleshooting.

•  If you find the end tabs keep popping out, add a small piece of tape on both sides of the joint.
• Use tacky glue and be sure it is dry before rotating your Flextangle! The glued joints are under stress so they need to be secure.
• Be sure to prime the Flextangle by rotating it slowly and popping out any unwanted bumps. The paper needs to flex a few times slowly before it rotates easily.
• Make sure the folds are creased well. I burnish the fold with the back of my thumb. When using card stock you may want to burnish the folds using your fingernail.

• Prime your flexagon by rotating it gently at first and pushing out any unwanted folds. Once it’s been rotated a few times it will loosen up.
• Standard printer paper makes the easiest to fold flexagons but they are not the most durable. Cardstock makes for more durable flexagons but you will need to really crease the fold lines or the model will be stiff.
• Younger children don’t have to pay attention to the tick marks, they will just enjoy coloring the template like my daughter did!

Flexagons are paper models that can be flexed to reveal hidden faces. They were originally created by Princeton graduate student Arthur Stone in 1939 and became a huge fad when Martin Gardner published them in The Scientific American years later. There are an incredible number of flexagon types. To try some other versions go here.

The model we have made here today is nicknamed a Kaleidocyle and because it’s not flat I’m not entirely sure it can be classified as a flexagon, but it certainly is loads of fun!