Cartesian/parametric equation of a 2v and 3v geodesic sphere

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Well.

I'm looking for the cartesian -or parametric- equation that describes the geodesics of 2V and 3V geodesic spheres. I'm not sure if I'm getting the terminology right, but what I'm looking for, essentially, are equations which I can plug values into, and it will describe for me the skeleton of a geodesic dome. I've tried googling this, but I haven't found anything appropiate.

Thanks in advance.