In 1939 a Princeton graduate student, Arthur Stone, played around with a strip of paper trimmed from his notebook and created the first flexagon. A flexagon is a polygon, usually made from paper, that can be folded in certain ways to produce a series of faces.

If that description didn't make any sense, you have two options: visit the homepage of David King and look at his very excellent Java Flexagon Animation . Otherwise you can continue reading and it should all make sense after constructing one yourself.

There are many different varieties of flexagons. The specific name of each flexagon has two prefixes, the first stating how many faces can be made to appear, and the second giving the shape of the flexagon. For example, a trihexaflexagon is in the shape of a hexagon and it has three different faces that may come up while folding; a hexatetraflexagon is shaped like a square or rectangle and has six different faces. That's all there is to it.

On this page you will find instructions on folding four different types of hexaflexagons. In addition, David King has generously let me use his instructions, which I have colored for your convenience. Triangles that are the same color end up on the same face when the flexagon has been constructed (with the exception of the gray faces, which are the two ends glued or taped together in the last step of each construction). Also provided for your benefit are .gif files (thanks again to David King!) that may be printed and cut out, saving you the trouble of trying to draw all those triangles yourself.

General instructions for the diagrams

How to flex (fold) your flexagon


Trihexaflexagon ---- printable model

Tetrahexaflexagon ---- printable model

Pentahexaflexagon ---- printable model

Hexahexaflexagon ---- printable model

Tuckerman traversals

David King's Flexagon Page
(includes flexagon theory articles. excellent page!)

General instructions

First of all, fold along every crease line on the strip, back and forth, ready for easy flexing.

For convenience, you may wish to number the sides according to color.

Now start at step 1. and go through each step in order. Each step (except for the third-to-last) has a heavy line with 2 faces marked u and d. Fold along the heavy line, so that after the fold u faces up and d faces down onto the table.

In one diagram, there is a triangle underneath y. Tuck the mini strip x and y beneath this, so you can only see x.

In the second to last diagram, stick the two faces u and d together with glue or double sided tape.

How to flex (fold) your flexagon

First, pinch together two triangles at a corner of the hexagon. Push the opposite corner down and in towards the center. You can now open out the middle to reveal a new face.

If you can't get it to work, try the next corner.

Tuckerman traversal

This term refers to the following diagram that shows the different sequences in which faces may appear while flexing a hexahexaflexagon. Each circle contains two different colors which correspond to the sides of one possible orientation of the hexaflexagon. All the different orientations possible by a single flex are those circles connected by lines.


printable model


printable model


printable model


printable model

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