Build a Flexagon Paper Toy

You have all seen movies that have shape-shifters or transformers in them. They are magical and wacky, as they change their shape at the drop of a hat. Today we are making a project out of paper called a Flexagon that is like a transformer. It is a paper puzzle craft that kids absolutely love!

Flexagon Paper Toy Craft & Math Lessons

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Would you believe me if I told you that there’s a paper puzzle craft that’s a shape-shifter in disguise?

Well, the flexagon, is a three-dimensional paper puzzle, which is made up of several connected triangles (hexaflexagons) or squares (tetraflexagons). It is a unique, magical, mathematical wonder!

This shape-shifter is made from a flat strip of paper folded into shapes like triangles, squares, or hexagons and when you “flex” (bend) it in different ways, hidden sides show themselves just like magic.

History of the Flexagon

In 1939, a student named Arthur Stone moved from England to America to study at Princeton University. While he was working with paper, he discovered that the paper in America was a different size to what he was used to. So, he trimmed the paper and with the leftover strips, he started playing… and folding. Eventually, Arthur folded the strips into triangles and glued them into a loop.

He discovered that when he bent and twisted it that something amazing happened – a new side popped out that he hadn’t seen before!

Arthur had discovered a flexagon, a flat paper shape that can be flexed to show hidden faces!

Flexagon Types

There are a few different types of Flexagons.

Triangle Flexagons are simple and perfect for beginners and are flat.

Hexaflexagons are a little more complicated and are three-dimensional. They have hidden sides that show themselves when they are flexed. This type of flexagon is what we will be making.

Pentaflexagons are harder to make but also have hidden sides.

All flexagons can be made with many different themes in mind. The one we will make today is celebrating nature.

Flexagon Lessons

Flexagons are great for teaching math and geometry through play and discovery. They help kids learn patterns and symmetry by letting them see and feel how shapes and colors repeat and change as they flex the flexagon.

Here’s how. Every time you flex a flexagon, a new side appears in a predictable order. As they flip, they start to notice: “After blue comes yellow!” “Then red shows up again!” This teaches pattern recognition which is an important math skill.

Learn more about 3D Geometry and Nets with this fun learning center concept.

Flexagons are made of identical shapes (like triangles or squares) that repeat over and over. This demonstrates how repetition creates structure and patterns which we also see in math, art, or music.

Symmetry is also a big part of this project. Flexagons have faces that are symmetrical, which means they look the same on both sides if you fold them in half. As students decorate or flex them, they will notice that a specific shape is the same on both sides and that it is mirrored. When the kids play with a Flexagon, the action helps them understand symmetry in a physical, memorable way.

With this project, kids can also flex their creativity by making their own designs and patterns on the flexagon faces. Then, when they flex it, they can see how the pattern travels and changes. Flexagons are like little puzzle-toys that turn patterns and symmetry into play and make great STEAM crafts for kids of all ages.

Discover more No Prep Paper STEM Activities!

So, grab your paper and scissors because in this amazing geometry project, you are going to mix art, math, and craft into one fun activity!

Making a Flexagon Math Toy

Materials

Scissors
Glue
Ruler
Cardstock and a printer to print the templates on cardstock
A ball-tool or a bone-folder for scoring. You can use the back side of one of the scissors blades.

Directions

Start by printing out the template you have chosen on cardstock. If you have chosen a blank or uncolored template, color it in now.

Cut the template out on the outer solid lines with scissors. Gently score all the dotted lines with your chosen scoring tool. The scoring makes it easier to fold and glue the flexagon together.

Double check that you have scored all the lines before folding. We need nice, crisp edges on the fold lines.

When folding, fold all the folds that are in the same direction, one after the other and then all those in the next direction and so on, this way you will not leave any lines unfolded.

Turn the template upside down and gently fold it into a tube before gluing together.

Starting at one end, put some glue onto the areas that are marked “GLUE” and glue the sides together. You may need to hold it for a minute or two for the glue to dry. Do not be in a hurry!

Pro Tip! Folding the two” pyramids” gently together for a few seconds, helps it keep its shape.

Move onto the middle section and then the last section in the same way as the first.

The last step is to squeeze some glue onto each of the “TABS”. Hold one end in one hand and the other in the other hand. Gently squeeze each end to make an oval hole and slide the “TAB” side into the other end until the two sides meet. Hold the ends gently together for a minute or two to dry.

Pro Tip! Put the flexagon down to dry properly before flexing it. You do not want it to fall apart while you are playing with it!

Now that it is dry, FLEX away and watch the magic happen!!!!!

Flexagon Ideas

Challenge your students to use one of the templates and design their own themed flexagon.

• Seasons and Holidays: Create one to go with the current season or holiday.
• Geometric Patterns: Create designs that use shapes like triangles, squares, and hexagons.
• Abstract Art: Experiment with different color combinations and patterns.
• Nature: Create designs inspired by ecosystems or landscapes.
• Hidden Messages: Create secret messages, codes, or puzzles that are revealed when the flexagon is flexed.
• Personalized Designs: Create flexagons that reflect your personal interests, hobbies, or memories. You can include images, drawings, or even personal quotes.
• Emoji Art: Use different emojis on each side

Now that you understand what flexagons are, try making one of the other kinds of flexagons.

Have fun exploring the magical world of flexagons and the art of paper-folding!

Extension Ideas

Set up a learning center where kids can play and explore with 3D Nets and geometry.

Dive into a fast, fun, and easy No Prep Paper STEM Projects.

Discover all the different ways you can use paper to make toys!

Feeling festive? Try Geome-Tree for some Christmas themed geometry challenges.

Put those geometry lessons to the test by building a treehouse in our Geometry Treehouse challenge.

Love origami? Make some Origami frogs that jump, and play some froggy math games.