We use the Valentiner action of $\mathcal A_6$ on $\mathbb C \mathbb P^2$ to develop an iterative algorithm for the solution of the general sextic equation over $\mathbb C$, analogous to Doyle and McMullen's algorithm for the quintic.
"Solving the sextic by iteration: a study in complex geometry and dynamics." Experiment. Math. 8 (3) 209 - 240, 1999.