How to make an octahedron from paper

The following is an excerpt from a beautiful page, which contains lots of nice and very explicit examples on how to do geometry with paper and scissors and a few other things.

Cut out four copies of the following stripes:
Streifen fuer Oktaeder
Larger versions of this stripe, which you can print out, can be found here either in PostScript or in pdf. If you have the stripes, fold upwards along the dashed lines.

Put two of the paper stripes (as shown in the first step of the following image - the German word "Schritt" means step) on top of each other in such a way that the stripes are curved towards the table. Attach the two top triangles with the help of a paperclip.
Netz zum Oktaederbasteln
Now, fold the stripes to form a double pyramide (as shown in the second step of the image), by putting the middle triangle of the left stripe below the middle triangle of the right stripe, and the bottom triangle of the right stripe below the bottom triangle of the left stripe. Fix the triangles with another paperclip. Repeat this with the other pair of stripes.

Put the second double pyramides (as shown in step three of the image) on top of the first. The arrows indicate the next steps in the procedure. Alread after the first of the remaining steps you obtain an octahedron, which is then further stabilized by performing the final steps. The last remaining flap should be plugged into the corresponding slot of the model.