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How to make a hexaflexagon
by nerdnurture on March 21, 2008
Table of Contents
How to make a hexaflexagon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
Intro: How to make a hexaflexagon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Step 1: Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Step 2: Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Step 3: Find center line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Step 4: Mark the center line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Step 5: Connect the dots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Step 6: Mark out scrap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Step 7: Crease folds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
Step 8: Fold the flexagon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Step 9: Glue the flap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Step 10: You are done! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
Related Instructables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Intro: 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... (-;
Image Notes
1. Mutualism is one of three kinds of symbiosis. This is a perfect study tool for
remembering three categories of things.
Image Notes
1. The magic happens right here. See how the other face is just trying to peek
through here?
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Image Notes
1. pull it open there in the middle and you get a hidden side. Do it again for the
third side.
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.
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
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. (-:
Image Notes
1. this is the third point in the equilateral triangle.
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.
Image Notes
1. These dots are 4 cm apart.
2. These are also 4 cm apart, but they fall half way between the dots on the edge
of the paper.
3. The two halves of the paper are equal in size (3.6 cm)
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Step 5: Connect the dots.
Draw diagonal lines to connect the dots. You will have 2 rows of alternating equilateral triangles.
Image Notes
1. This is the intersecting arc I made a few steps ago.
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.
Image Notes
1. 10 triangles on top
2. 8 triangles on the bottom
3. I guess it could start out as a 20 cm strip of paper, but I like to have some goof
room.
Image Notes
1. Triangle #1
2. Triangle #10
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.
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Image Notes
1. These tiny glue sticks are great! They are cheap, and run out of glue before I
have to clean out the nozzles and dig in the box for caps!
Image Notes
1. The folded edge.
Step 8: Fold the flexagon
You will fold the flexagon by making the starred sections touch each other.
Image Notes
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Image Notes
1. Make these two touch each other.
1. Now fold these to touch each other.
Image Notes
1. This is after you make the two stars touch.
Image Notes
1. Now flip the whole thing over so you can see the other pair of stars.
2. Fold these two to touch just like the others.
Image Notes
1. Just like that.
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.
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Image Notes
1. Here, the left flap is over the right flap.
Image Notes
1. What we want is the right flap to be on top of the left flap.
Image Notes
1. Now put some glue between the flaps.
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!
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Image Notes
1. Push down the sides, while trying to arrange the whole thing to make this
upside down Y.
Image Notes
1. When you pull apart from the middle, it opens up to a new hexagon. You can
repeat this step once more to see the third side.
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Comments
45 comments Add Comment
sofialicky123 says:
Aug 28, 2010. 8:44 AM REPLY
your right! i do too!why??
Michael Pawlicki says:
Dec 17, 2009. 5:31 PM REPLY
it didnt say anything about a compass in the materials
LiMiT-L3sS says:
Mar 7, 2010. 9:38 PM REPLY
Dont listen to the dude who made this instructable he got mixed up or he's Brittash
nerdnurture says:
Mar 8, 2010. 4:55 AM REPLY
Why do my commenters always assume I'm a man?
*gasp*
Do I have man-hands???
LiMiT-L3sS says:
Jul 18, 2010. 8:05 PM REPLY
sorri plz repli
nerdnurture says:
No prob! (-:
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Jul 18, 2010. 10:08 PM REPLY
LiMiT-L3sS says:
Jun 6, 2010. 6:33 PM REPLY
sorry i always say that to anyone OK nerdnurture
nerdnurture says:
Dec 17, 2009. 6:34 PM REPLY
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!
mushroom1225 says:
Jun 26, 2010. 12:36 PM REPLY
Im confused, did you take the pictures off, because there not on my computer
KDB955 says:
Apr 1, 2010. 12:18 PM REPLY
Would you guys pay attention!!!1!
He keeps telling you he's female.
Besides, only girls read L'Engle.
ktpjfarrell says:
Mar 12, 2010. 11:20 AM REPLY
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 says:
Mar 15, 2010. 3:26 PM REPLY
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 says:
Mar 15, 2010. 2:28 PM REPLY
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 ._. says:
Jan 20, 2010. 8:06 PM REPLY
Why can't we just make a dot below the mid point of the 4 cm dots, instead of making those crosses?
Salsa766 says:
Dec 18, 2009. 2:40 PM REPLY
omg i just finished an exam today on symbiosis!
mightywombat says:
Jul 25, 2008. 10:04 AM REPLY
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 says:
Jan 8, 2009. 2:46 PM REPLY
be thankfull he put it on google
nerdnurture says:
Nov 10, 2009. 5:07 PM REPLY
he's a she. (-;
Rock Soldier says:
Nov 30, 2009. 1:49 PM REPLY
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 says:
Nov 10, 2009. 3:05 PM REPLY
google?
this is instructables.
LuckazMARTINS says:
Try YOSHIMOTO CUBE
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Nov 29, 2009. 6:33 AM REPLY
andygold says:
Nov 22, 2009. 7:52 PM REPLY
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 says:
Nov 22, 2009. 9:06 AM REPLY
BEASTIE
Mikey D says:
Nov 10, 2009. 10:32 PM REPLY
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!
Mikey
nerdnurture says:
Oct 13, 2009. 6:54 PM REPLY
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 says:
Oct 13, 2009. 6:03 PM REPLY
why do you say protractor, but have a compass?
rymagiccraft123 says:
Sep 23, 2009. 10:19 PM REPLY
that is so hard !!!!!!
llamadudeguy says:
Jun 13, 2009. 11:12 AM REPLY
this is so cool! ima show it 2 all my friends. + i voted u
mikemmcmeans says:
Jul 27, 2008. 6:08 PM REPLY
make a video
nerdnurture says:
Aug 2, 2008. 12:14 PM REPLY
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 says:
Jan 8, 2009. 2:45 PM REPLY
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 says:
Sep 9, 2008. 6:48 PM REPLY
I'll figure it out and make one
Arbitror says:
Nov 7, 2008. 10:19 PM REPLY
A printable pdf would be nice.
nerdnurture says:
Nov 8, 2008. 7:12 AM REPLY
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 says:
Yeah, but what about people who look for cool stuff to do without a lot of effort? (like me)
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Nov 23, 2008. 6:29 AM REPLY
nerdnurture says:
Nov 23, 2008. 8:32 AM REPLY
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 says:
Jul 24, 2008. 11:19 AM REPLY
awesome! I found a site with instructions for a flexagon with 4 sides though more it's complicated
Four Faced Flexagon
robocrazy155 says:
Jul 24, 2008. 11:20 AM REPLY
(Though it's more complicated) sorry
nerdnurture says:
Jul 24, 2008. 9:31 PM REPLY
Thank you for the link! Very interesting.
15zhangfra says:
May 28, 2008. 1:49 PM REPLY
great although i don't use this for studying, its great fun just to flip around:)
Vinstepula says:
Mar 28, 2008. 11:44 AM REPLY
I hate note cards, sadly I use them a lot because it is one of the few ways that I can learn. I really love your idea because the cards look nice (and they have
an awesome name). I know that I will use these in college. You get a vote from me!
GorillazMiko says:
Mar 22, 2008. 8:56 PM REPLY
Wow, this is so cool. I've never even heard of a hexaflexagon, but it's cool. +1 rating and vote.
nerdnurture says:
Mar 23, 2008. 8:19 AM REPLY
Thanks for the votes! (-:
burzvingion says:
Mar 21, 2008. 8:44 PM REPLY
I've never been a fan of note cards, but this is just too fancy not to like.
nerdnurture says:
Thanks! I'm glad you like it. Note cards are boring. How's about a vote? (-;
http://www.instructables.com/id/How-to-make-a-hexaflexagon/
Mar 22, 2008. 8:35 AM REPLY