Introduction: How to Make a Hexaflexagon

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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 www.flexagon.net. 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!

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