  We consider the space $P$ of generic complex 5-degree polynomials. Critical
values of such polynomial, i.e. four points in the complex plane, either are
vertices of a convex quadrangle $Q$, or vertices of a triangle $T$ with one
point inside $T$. The inverse image of $Q$ is a tree-like connected structure
of five ovals (a cactus). The inverse image of $T$ is also a cactus, but of
four ovals. Transformations of cacti of the first type into cacti of the second
type and vice versa allow one to represent the space $P$ as a ribbon bipartite
graph of genus 3.
