Hexaflaxagons are masterpieces of geometry that you can create in a matter of minutes! I learned how to do this from my math teacher and have made a lot since then with my friends, and now you can make them too!!
Step 1: Supplies
Here is what you will need to create your hexaflexagon:
-paper, use bright colors to make it prettier
-scissors (WARNING: do not run with)
-paper cutter that cuts straight lines in paper
Step 2: The Cutting
Line up the paper in the paper cutter and cut out a strip of paper that is about 1 1/2 inches wide. This is all you need from the paper, so make a paper airplane or something with the leftover paper :P
Step 3: The Folding
Fold a small fold on the top that makes the tip pointy as seen in the first picture. After that, fold it to the right so it lines up with the edge as seen in the second picture. Now, flip the paper over and make the same fold as the previous one on the other side as seen in the third picture. Continue this process of flipping it over after every fold until it looks like a tiny triangle accordion with a little bit of paper sticking out, as seen in the last picture. You are now done folding.
Step 4: More Cutting!
This part is simple. Just unfold the paper and cut off little triangles until there are only nine left. The triangles will be easier to see on your hexaflexagon because they don't show up too well in the pictures.
Step 5: Almost Done!!
This final part is tricky. Take one end and Fold one triangle up. Then take the other end and fold it two triangles in. Then take the side with one folded and fold it over to the other side, so it looks like a hexagon. This part is really hard to explain, so study the pictures and experiment. Once that is done, take a piece of tape about an inch and a half long and put it where my finger is on the last picture to keep it from coming undone.
Step 6: You're Done!...how Does It Work?
Now that you are done, lets find out how to use it. Draw a face or something, preferably not in sharpie like I did because it bleeds. Then fold it outward so it looks like a triangle with points, then sort of grab the middle and turn it inside out. Now you have a brand new empty side! You can draw something else, and still do that one more time! After you get to the third side, do it again to find yourself back at the first side.
Don't worry if your hexaflexagon is messy, they will improve as you make more! Try making different sizes and different designs on your own! I hope you enjoy your hexaflexagons as much as I do!