We can now describe Klein's invariant function ℑ that equals 0 at the centers of the icosahedron's faces, 1 on the midpoints of its edges, and ∞ at its vertices.

The polynomial F has degree 20, while V has degree 12.
Thus both F³ and V⁵ have degree 60, so

F³ / V⁵

is homogeneous of degree zero, giving a well-defined rational function ℑ: ℂP¹ → ℂP¹.

ℑ = 0 at face centers and ℑ = ∞ at vertices. By symmetry ℑ takes the same value at every edge midpoint. We can normalize F, E and V to make this value be 1.