In this paper we study the 5 families of genus 3 compact Riemann surfaces which are normal coverings of the Riemann sphere branched over 4 points from very different aspects: their moduli spaces, the uniform Belyi functions that factorize through the quotient by the automorphism groups and the Weierstrass points of the non hyperelliptic families.
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Yolanda Fuertes, Manfred Streit, Genus 3 normal coverings of the Riemann sphere branched over 4 points. Rev. Mat. Iberoam. 22 (2006), no. 2, pp. 413–454DOI 10.4171/RMI/462