A flexagon is a polygon made of paper folded in a way that allows three patterned faces to be exposed. To make one, you are going to need some paper, a template, scissors, and glue. By folding it carefully, you can make your own flexagon and impress your friends with your new geometric toy. Besides being an educational project, it's also a lot of fun!
Part 1 of 3: make a flexagon
Step 1. Print a template
Search online for “flexagone”, “hexaflexagone” or “tri-hexaflexagone” to find a model. You should be spoiled for choice among all the models you are going to find. Pick the ones you like best and print them out.
You can also print a blank template and color it as you like
Step 2. Cut out the template
Take scissors and carefully cut along the outer lines. Try to cut as straight as possible and directly over the lines. It is important to cut them accurately so that it bends properly.
It is recommended to use the scissors under adult supervision
Step 3. Mark and fold along the center line
Once you have cut out the model, you will need to make several folds to complete your flexagon. The first fold should be made along the center line. Mark this line with an empty pen by putting a ruler down and running the pen all the way. This step will make it easier for you to fold the next step.
- Fold the model so that the patterns are on top.
- Once you've made the crease, run the ruler all the way down to mark the edge.
- Run the glue stick along the shorter half of the pattern before gluing it on the longer half.
Step 4. Mark and fold along the edges of each triangle
Once you've glued the two edges together, mark the edge of each triangle. Fold it back, then forward along the edges of the black lines.
This fold marking step will allow you to fold the flexagon more easily
Step 5. Make a four-triangle fold from the right
At this point, you should end up with the smaller edge on top. You should see two white triangles on both sides with eight patterned triangles in the middle. Count four triangles from the right of the paper and fold along the far edge of the fourth triangle (in fact, this is the third patterned triangle, because there is a blank triangle at the end).
Make the crease down so that the crease points up
Step 6. Make another four-triangle fold from the other side
Turn the sheet of paper over and count four triangles from the left of the model. Fold the paper upwards so that it begins to take the shape of a hexagon. If you've folded the pattern well so far, you should only see one pattern, resulting in a hexagon with a triangle sticking out.
If you haven't made the right folds, just unfold it and start over
Step 7. Fold and glue the additional triangle onto the hexagon
Take the protruding blank triangle and fold it over the other blank triangle. You should end up with a hexagon with six identical faces. Glue the triangle in place.
- If you flip the flexagon over, you should see another pattern with six identical sides on it.
- The third pattern is hidden on the back sides of the two visible patterns. When you fold the flexagon, you should see the third pattern.
Part 2 of 3: use the flexagon
Step 1. Fold and unfold along the three diagonals
It takes a bit of practice to manipulate the flexagon, but it will be easier if you bend and unfold it several times. Make folds along the three diagonals of the hexagon and fold it back and forth several times.
This step is not absolutely necessary, but it will be easier for you to play with your flexagon if you do
Step 2. Pinch two contiguous triangles
Fold two triangles that are touching so that the fold goes towards the inside of the flexagon. The other two sides should flatten against each other.
The more you use your flexagon, the easier it will be to handle it
Step 3. Unfold the new pattern from the flexagon
Once the two triangles are pinched towards the middle, the flexagon should almost open on its own on its new pattern. Grab the top corners of the flexagon and pull them together to reveal the new pattern.
Practice opening and closing the flexagon to see the three patterns
Part 3 of 3: create your own pattern
Step 1. Print a blank flexagon template
Make sure the pattern is numbered to indicate the triangles that will make up the pattern. The model will consist of a series of numbered triangles according to the corresponding side.
- A trihexaflexagon will have triangles numbered 1, 2 and 3.
- A hexa-hexaflexagon will have triangles numbered 1 through 6, as there will be six different patterns.
Step 2. Decorate the model according to the numbered designs
You can let your imagination run wild. Make sure to color all the triangles with the same number in the same way. You can also print a patterned image and cut out triangles before gluing them to your model.
For example, all triangles with number 1 are red, all triangles with number 2 are green, and all triangles with number 3 are blue
Step 3. Try different shapes
There are many different types of flexagons. You can create them with numbers on the sides and different patterns. It is impossible to describe all the possible shapes in this article, but you can create any shape you want by printing the template and folding it correctly.