Geodesic
Belyi function decompositions for the icosahedron of genus~$4$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 3-30.

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The icosahedron $I_4$ of genus $4$ is a dessin d'enfant embedded in Bring's curve $\mathcal{B}$. The dessin $I_4$ is related in some sense to a regular icosahedron $I_0$ embedded in the complex Riemann sphere. In particular, decompositions of Belyi functions $\beta_{I_0}\colon \mathbb{CP}^1 \rightarrow \mathbb{CP}^1$ and $\beta_{I_4}\colon \mathcal{B} \rightarrow \mathbb{CP}^1$ for $I_0$ and $I_4$ have the same lattice. The diagram of $\beta_{I_0}$ decompositions is already known. In the present paper we find $\beta_{I_4}$ decompositions. Note that $\beta_{I_0}$ decomposes into rational functions on $\mathbb{C}P^1$, while in case of $\beta_{I_4}$ we deal with maps between different algebraic curves. 
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N. Ya. Amburg; M. A. Kovaleva. Belyi function decompositions for the icosahedron of genus~$4$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 3-30. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a0/

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