For an octahedron you need 240 beads: 144 for the edges and 96 for the faces.
To begin, you need to build several triangles. Can you guess how many?
Click here to see how to make triangles.
Have you made all the triangles you need?
Now take three of them and try to make a triangle between them. This time you have to use the edge beads of those 3 triangle as the edge beads of your new triangle:
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The pictures above just show you how I managed to make the new triangle in the middle. You can follow the pictures to do it like me, or do it in any other way you have found.
Now you are ready to complete your octahedron. It is going to look like this:
The last triangle is going to be a little tricky. I've included step-by-step pictures of me making the last triangle to help you:
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Uh Oh! What is that?
Where are the rest of the scissors?
Congratulations! Your octahedron is now ready. Here is mine: