How to Make a Hexaflexagon




This is another magic pocket study tool I teach my students how to make. It is what is called a trihexaflexagon, which means basically a hexagon you can turn inside out to reveal a total of 3 complete faces (or sides of the paper). They put notes on these things and keep them in their pockets to make use of those odd bits of otherwise wasted time during the day (watching commercials during Channel One, waiting for the Pledge of Allegiance, after you finish your classwork...). Find enough odd bits of time, and you are done studying before you ever even get home! Now go have fun!

This is my second instructable. Clearly the first one wasn't exciting enough to win me a T-shirt... (-;

Step 1: Materials

For this project, you need a sheet of paper, a ruler, a protractor, scissors, and glue.

Step 2: Measure

Your paper needs to be trimmed down to 24 cm across. Then mark every 4 cm along the top edge of the paper. Really, you could make this any size you want, since you use the protractor to measure the right proportions. But I like a flexagon this size, and it's easy to count by 4s. So that's how we do it. It's not important though.

Step 3: Find Center Line

Set your compass to measure between the markings (4 cm). Place the point of the compass on the first marking. Draw a short arc. Move the compass point to the next marking, and draw an arc which intersects the first one.

This seems a little obvious, since a flexigon is clearly a mathematical wonder. But I have to say it anyway. This is also an awesome lesson to use for math instruction. I try to cruise through the steps as fast as possible, so it actually gets used for MY intended purpose - as a pocket study tool. But it sure would be fun to really delve into the geometric principles behind it... But alas, I am not a math teacher. (-:

Step 4: Mark the Center Line.

The point where the two arcs intersect marks where you will draw a horizontal line parallel to the top edge. If your paper is 24 cm wide, and your markings are 4 cm apart, this will be about 3.6 cm away from the top edge of the paper.

Draw this horizontal line, then fold the paper along that line. This will allow you to cut the sheet of paper so the top half and bottom half are now equal.

Now mark along the center line every 4 cm starting at the 2 cm mark.

Now mark the bottom edge just like the top edge - every 4 cm.

Step 5: Connect the Dots.

Draw diagonal lines to connect the dots. You will have 2 rows of alternating equilateral triangles.

Step 6: Mark Out Scrap.

Mark out what will not be used. Then cut out the scrap.

Now make some special marks on the two center triangles in the bottom row, and triangles #2,3,8 and 9 in the top row. These will help you fold the whole thing together, but you'll want to erase them later.

Step 7: Crease Folds.

Fold diagonally on all of the lines. Do both a mountain fold and a valley fold on each one. Then fold the whole thing in half along the horizontal line.

Glue the thing shut while folded horizontally.

Step 8: Fold the Flexagon

You will fold the flexagon by making the starred sections touch each other.

Step 9: Glue the Flap

You will glue the flaps together, but first reverse their positions so that the one that was on the bottom is now on the top.

Step 10: You Are Done!

Now flex it! Push in the sides so you get a Y shape, then pull out from the center to reveal the hidden sides. Think of how to categorize what you need to study into three groups, then write your notes on the flexagon. Stick it in your pocket, and you're ready to go!

Disclaimer - Many people apparently know how to make flexagons, and I don't remember where I learned how. I recently found a site with many many cool versions of this mathematical piece of magic. It is I have been using flexagons for years in my classroom and, to my knowledge, I am the only person who uses them for this purpose. If you know otherwise, please let me know!

Participated in the



    • Growing Beyond Earth Maker Contest

      Growing Beyond Earth Maker Contest
    • Stone Concrete and Cement Contest

      Stone Concrete and Cement Contest
    • DIY Summer Camp Contest

      DIY Summer Camp Contest

    57 Discussions


    2 years ago

    I messed up. I don't know what happened but it looks like your thing but I won't make a Y shape and whenever I flip it half of the triangles stay on the same side


    3 years ago

    Very easy made it all by myself


    Reply 3 years ago

    excuse me, what's wrong with being british?


    Reply 9 years ago on Step 1

    Why do my commenters always assume I'm a man? 


    Do I have man-hands??? 

    nerdnurtureMichael Pawlicki

    Reply 9 years ago on Step 1

    Hey, I've already confessed my compass crime.  But just in case you're holding it against me because you don't have a compass, you can make your own with a thumbtack, a strip of cardboard, and a pencil.  Maybe the subject of my next instructable, if I ever have time!


    4 years ago on Introduction

    Guys just watch this video


    5 years ago on Step 9

    on the internet no one knows your a potato


    5 years ago

    teachers like you are what makes school tolerable. things like this we're perfect wouldn't me when I was young cuz I was so energetic and could not sit still. I disrupted every single class I was in the teachers always said they loved me but they just couldn't stand to have me in their class cuz I would not sit still or shut up. the teachers I remember the most are ones that came up with projects like this for me because it kept me busy. keep up the good work your students will remember you.


    6 years ago on Introduction

    Please answer to my question: How to glue this? (Step 7) "Glue the thing shut while folded horizontally." doesn't help. All triangles? I glued all triangles, but it doesn't work. (Or I really don't know how to "pull out from the center". I have a pink side and i pull out from the center and I have the same side!!! Please help me! ;( I'm very frustrated right now!! )

    1 reply

    Reply 5 years ago on Introduction

    it means to fold it like this

    a is the top of your paper and b is the bottom.
    you fold from a to b to a and glue them together ( i hope that makes sense )
    But, I can't really explain how to flip it... sorry :(
    Check youtube. it might help