Xu's surface with icosahedral symmetry

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Weierstrass Data

\[ M=(\mathbb{C}\cup\{\infty\})\setminus\{z\in\mathbb{C}\;;\;z^{20}-228z^{15}+494z^{10}+228z^5+1=0\}, \] \[ g=\frac{57z^{15}-247z^{10}-171z^5-1}{z^{19}-171z^{14}+247z^9+57z^4},\quad \eta = \left(\frac{z^{19}-171z^{14}+247z^9+57z^4}{z^{20}-228z^{15}+494z^{10}+228z^5+1}\right)^2dz. \]