One advantage is that you can use arbitrary N. If you just want N in a certain range, we can use the triangle-based polyhedron and successively quadruple or tr

One advantage is that you can use arbitrary N. If you just want N in a certain range, we can use the triangle-based polyhedron and successively quadruple or triple the number of faces. Then use the face normals as points. This gives visually appealing distributions without any real oddities.