Fourth

Sphere::Sphere(int n) : Shape() {

    //no factor greater than 5 (far too long computation time)
    if( n > 5 )
            n = 5;

    float five = 5.0;
    float a = 2.0 / ( 1.0 + sqrt(five) );

    Vector3 origin(0,0,0);

    //icosahedron vertices
    Vector3 tv0(0 , a, -1);
    Vector3 tv1(-a, 1, 0);
    Vector3 tv2(a, 1, 0);
    Vector3 tv3(0, a, 1);
    Vector3 tv4(-1, 0, a);
    Vector3 tv5(0, -a, 1);
    Vector3 tv6(1, 0, a);
    Vector3 tv7(1, 0, -a);
    Vector3 tv8(0, -a, -1);
    Vector3 tv9(-1, 0, -a);
    Vector3 tv10(-a, -1, 0);
    Vector3 tv11(a, -1, 0);

    //create the triangles in the original mesh
    vector< vector<Vector3> > triangles;

    for each triangle in the icosahedrion
        create that triangle and add it to the triangles vector

    //so we have all of the vertices in there original coordinates
    //with that, we subdivide each polygon into 4 new ones and
    //do this n number of times
    for( int i = 1; i < n; i++ ) {
            vector< vector<Vector3> > tempTriangles;
            for( int j = 0; j < triangles.size(); j++ ) {
                //now we subdivide
                vector<Vector3> triangle = triangles.at(j);
                Vector3 two = triangle.at(2); //point 2 of the triangle
                Vector3 one = triangle.at(1); //point 1 of the triangle
                Vector3 zero = triangle.at(0); //point 0 of the triangle
                Vector3 a( ((two+zero)*.5) ); //intermediate point a
                Vector3 b( ((one+zero)*.5) ); //intermediate point b
                Vector3 c( ((two+one)*.5) ); //intermediate point c

                add four the new triangles to the temp container

            }
            triangles = tempTriangles;
    }

    normalize each triangle vertex (hint: use the temp container here again)

    create triangles in the order we get them out of the triangles container

}