Hexaflexagons and how to fold them

What is a hexaflexagon? Yes, it is a real thing. At first glance, a hexaflexagon appears to be a simple two-dimensional two-sided hexagon. However, if you know how to fold it the right way, it can be rearranged to reveal a third side hidden within.

Image taken from: http://vihart.com/hexaflexagons/

How do I create a hexaflexagon? They are actually quite simple. First, you’ll need to start with a strip of paper. Fold it over itself to create a chain of ten equilateral triangles. You’ll know that the triangles are equilateral if they can continue to be folded on top of one another while still staying within the sides of the paper strip.

Then you have to fold it into a hexagon shape as shown below, making sure to have the three openings facing the same way. There also shouldn’t be an opening all the way through the middle of the hexagon.

Once it is folded correctly, either fold and glue the tenth triangle, or cut off the tenth triangle and instead use tape on the seam.

Once you have your hexaflexagon made, you can color it so that once the third side is revealed it is obvious that it is a new side. To reveal the third side, pinch three of the seams inward. Then open the seams along the top. If you can’t find the opening to the third side, try flipping the hexaflexagon over and doing the same process again. Below is a diagram of how to reveal the third side.

Image taken from: https://home.adelphi.edu/~stemkoski/mathematrix/flexagon.html

The hexaflexagon mentioned above is actually known more specifically as a trihexaflexagon because it has three sides. You can also create hexahexaflexagons, which contain a total of 15 different arrangements, or tetraflexagons which are square shaped and are used to construct many things including the Jacob’s Ladder toy and the magic wallet trick.

If you want to learn more about hexaflexagons, print a template, or watch an instructive video, visit vihart.com/hexaflexagons