The FLEXAGON is a fascinating little toy. At first glance it appears to be a flat hexagonal disc with two sides. On closer inspection, you can fold it into itself then open it out again (like a flower) to reveal a third side. Depending on the design on these "surfaces", flexing the FLEXAGON again and again can appear to expose a total of six distinct sides. That in itself might seem weird but when you analyse it, you actually discover the shape you are holding has not six, not three and not even two sides. It actually only has one.
The designs shown on the graphic at the top of this page can be reproduced by a flexagon made with a single surface like this.



If you print this, cut it out, crease, fold and glue it right, it will make a flexagon with one side only.
Despite seeming to be quite complicated, the flexagon is, really, quite simple to make. All you need is a strip of paper and either a glue stick or some double sided sticky tape.
STEP 1

Cut a long strip of paper and crease 60 degree lines across it along its length.
You could try to measure the angle with a protractor or something of the sort but I find its actually quite an easy angle to judge by eye and once you get the first couple of creases done the rest just fall into place. You should end up with a row of triangles like this. Trim off the ends leaving ten connected triangles.



Counting both sides, that's a total of twenty triangles but there's going to be an overlap and two of them will be stuck together removing their surfaces from the final product which has 9 double sided sections.
STEP 2

A mobius strip is a one sided shape created by adding a single twist before joining the ends of a simple loop of paper. This shape also has only one side but instead of one twist, it has three.

With the strip flat on your worktop and counting from the left, fold the paper up at the crease joining the third and fourth triangles.

That's the easy bit and the first of the three twists.
STEP 3

The second twist is created by folding the strip down at the crease joining the sixth and seventh triangles.

You have to prepare for the third twist at this stage by tucking the folding strip under the first triangle.
STEP 4

The third and final twist is created by the overlap.

With glue or double sided sticky tape, fold the protruding triangle into the hexagon and stick it in place.
CONGRATULATIONS

You've made a flexagon.

Now all you have to do is decorate it and experiment with different designs to see what happens to them when they flex.