The octahedron was the first balloon I ever made. It is by far the easiest one to make since all the vertices have degree 4. There are many one balloon paths that construct the octahedron but the one I describe here is nice because it does not require a balloon to be pulled through a triangle.
To describe this I have the following youTube videos.
Here's the original with a 350 balloon.
The psuedo-gauss code for this is
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