by Wootfish, published
I made this model in sketchup following instructions found in the video http://mathforum.org/sketchup/videos.html. Bonnie Roskes (of 3DVinci) made this video, and has many other excellent sketchup tutorials on the site: http://mathforum.org/sketchup/index.html.
There is a nice page for this shape on Wikipedia as well: http://en.wikipedia.org/wiki/Stellated_octahedron
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In addition to following Bonnie's instructions, I had to remove the internal polygons that form the octagon in order to create a clean STL file. When I skipped this step, I ended up with a model with a hollow center - interesting, but risky to build.