Illustrator :: How To Convert Lines To Polygons

I am building a compass rose by using the star tool with 4 points and adding straignt lines from the end points to the corresponding end point.  Ultimately, I'll replicate the whole image with some scaling, copy it 3 times, and rotate each 22.5 degrees to create the final rose.
 
I want give some 3D effects by shading half of each point on the star but it's actually a polygon (the star) with a straight lines splitting the points.  To shade I need to have the star actually be 8 triangles that I can fill (4 of them).
 
Other than tracing to create one of the triangles (and then do some replacation and transforms to locate) is there another way to convert to star polygon and the straight lines into the triangles?
 
Using CS5.