I study the function $z\to \dfrac{z^3}{z^4+27}$. The branch points are $z=-3i,-3,0,3,3i$. I have $4$ copies of the sphere (degree of the rational function). And I calculate the monodromy group to know the permutation and determinate the copies that coincide in the branch points. See the figure.
my question is How i do made the cuts and glue for the copies? I try the planar representation of the Sphere. But i don´t now if this is correct. I cut from the lines and make a identification to glue the copies.
Please Help, sorry for my English