Introduction: How to Make a Hexaflexagon

Picture of 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

Picture of Materials

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

Step 2: Measure

Picture of 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

Picture of 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.

Picture of 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.

Picture of Connect the Dots.

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

Step 6: Mark Out Scrap.

Picture of 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.

Picture of 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

Picture of Fold the Flexagon

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

Step 9: Glue the Flap

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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!

Picture of 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!


Dogsforever (author)2017-01-24

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

TamaraT6 (author)2015-11-14

Very easy made it all by myself

Michael Pawlicki (author)2009-12-17

it didnt say anything about a compass in the materials

Dont listen to the dude who made this instructable he got mixed up or he's Brittash

MelC10 (author)LiMiT-L3sS2015-11-01

excuse me, what's wrong with being british?

The gun guy (author)LiMiT-L3sS2014-02-28

good thing you can really make a point by spelling British right -_-

nerdnurture (author)LiMiT-L3sS2010-03-08

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


Do I have man-hands??? 

LiMiT-L3sS (author)nerdnurture2010-07-18

sorri plz repli

nerdnurture (author)LiMiT-L3sS2010-07-18

No prob! (-:

LiMiT-L3sS (author)nerdnurture2010-06-06

sorry i always say that to anyone OK nerdnurture

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!

PiyushM (author)2014-09-11

Guys just watch this video

deedee239 (author)2014-04-14

yea it didn't say anything about a compass

potato325 (author)2014-02-26

on the internet no one knows your a potato

lcastro12 (author)2013-12-20


nbaze (author)2013-11-16

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.

Petra1999 (author)2013-03-08

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!! )

may37865 (author)Petra19992013-09-28

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

stud-work (author)2012-10-08

Thanks. Interesting.

freakyqwerty (author)2011-12-17

You should try some other variations and post ibles on how to make those!

sofialicky123 (author)2010-08-28

your right! i do too!why??

mushroom1225 (author)2010-06-26

Im confused, did you take the pictures off, because there not on my computer

KDB955 (author)2010-04-01

Would you guys pay attention!!!1!
He keeps telling you he's female.
Besides, only girls read  L'Engle.

ktpjfarrell (author)2010-03-12

 This is the first comment I have made!

What you are using is a pair of compasses!  A compass will get you home but is not a lot of use for drawing circles - I should be a teacher.

ktpjfarrell (author)ktpjfarrell2010-03-15

 I know, but I was reading through the comments and couldn't resist saying something - the basic point about how clever the flexagon actually is was buried which just made it funny - I mean you no harm!

nerdnurture (author)ktpjfarrell2010-03-15

Oh for crying out loud.  Again with the compass?

I have confessed my crime.

Yes, you should be a teacher.  Because that's all there is to it - just knowing the difference between a compass and a protractor.

w00t ._. (author)2010-01-20

Why can't we just make a dot below the mid point of the 4 cm dots, instead of making those crosses?

Salsa766 (author)2009-12-18

 omg i just finished an exam today on symbiosis!

mightywombat (author)2008-07-25

This is interesting, though I think probably more useful for elementary or high school study guides. I'm having a hard time seeing where I might use this for anything at the college level. Still, very cool flexagon!

hellogeek (author)mightywombat2009-01-08

be thankfull he put it on google

nerdnurture (author)hellogeek2009-11-10

he's a she.  (-;

Rock Soldier (author)nerdnurture2009-11-30

I love when people do that, except in real life, I'd have to say, She's a he.
(I have long hair. I get mistaken for a girl sometimes)

dagenius (author)hellogeek2009-11-10

this is instructables.

LuckazMARTINS (author)2009-11-29


andygold (author)2009-11-22

I used to make hexa-hexa flexagons.  They had 6 separate faces,  numbered 1 through 6.  Normally all you get was faces 1 through 4 to show up in a row, but I figured out how to get them from 1 to 6 in order without having to go through any other faces.

I still have some of them tucked away in a drawer since I was a kid.  Don't know why i saved them, but I've had them for 40 years.

cojo (author)2009-11-22


Mikey D (author)2009-11-10

Too cool!

We used to make these in Elemmentary school about a billion years ago.  We actually got up to a duo-decka-Hexa-flexagon (20 sides if I remember corerectly) but alas I have forgotton how to fold them.  We used adding machine paper and no guideline  but they worked fine.

I have brought this up in conversations many many times but no one seemed to know what I was talking about.  :-(.

Thank you for posting this!


nerdnurture (author)2009-10-13

Because clearly I don't know the difference between a compass and a protractor. I should have called it a circle thingie.   I should be relieved of my duties.  (-; 

Colne Fawkes (author)2009-10-13

 why do you say protractor, but have a compass?

rymagiccraft123 (author)2009-09-23

that is so hard !!!!!!

llamadudeguy (author)2009-06-13

this is so cool! ima show it 2 all my friends. + i voted u

mikemmcmeans (author)2008-07-27

make a video

nerdnurture (author)mikemmcmeans2008-08-02

Video wasn't working on the gooseneck in my classroom. Sorry if the pictures don't suffice. My students are able to understand these instructions, so I don't really care to redo the whole process again just to make a video. Sorry. Someone else can do it if they really want to. (-;

hellogeek (author)nerdnurture2009-01-08

I like your instructions and some people just don't have your classmates cinnda tallent. p.s im not trying to be mean guys

casey321b (author)nerdnurture2008-09-09

I'll figure it out and make one

Arbitror (author)2008-11-07

A printable pdf would be nice.

nerdnurture (author)Arbitror2008-11-08

It sure would, but part of the point of this project, for my students anyway, is to follow directions and study the geometry. There are places online where you can print templates. But I wanted to show how to make your own.

kibbler (author)nerdnurture2008-11-23

Yeah, but what about people who look for cool stuff to do without a lot of effort? (like me)

nerdnurture (author)kibbler2008-11-23

you can google hexaflexagon template and print away. But you probably can't find another set of instructions to mathematically construct your very own. Sorry. Not giving in on this one... LOL (-;

robocrazy155 (author)2008-07-24

awesome! I found a site with instructions for a flexagon with 4 sides though more it's complicated

Four Faced Flexagon

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