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A polynomial $p\in \mathbb{C}[z]$ with three finite values is called theZolotarev polynomial. For a class of such polynomials with the given degree,given passport and simple critical points we define a \emph{combinatorialmoduli space}. A combinatorial moduli space have the same essential propertiesas analytical moduli space, but much easier to construct. We study theseobjects for Zolotarev polynomials of degree 5, 6 and 7.

Zolotarev polynomials of degree 5, 6 and 7 with simple critical points and their moduli spaces