Haskell Quiz/Geodesic Dome Faces

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Given the faces of a triangle-faced platonic solid centered at the origin, and a number n, break each triangle side in n evenly distributed places, draw in the lines between these points that are parallel to the sides, and from each triangle thus drawn we can get a geodesic triangle by normalizing the position vectors to have distance 1 from the origin. The problem is to implement this.

The Problem