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Apr 26, 2023 at 13:27 comment converted from answer Nick Ulyanov Just wanted to add a small remark to Noam Elkies' answer — all of the mentioned polynomials above: \begin{gather*} A(x) = x^{20} + 228x^{15} + 494x^{10} - 228x^5 + 1 \\ B(x) = x^{30} - 522x^{25} - 10005x^{20} - 10005x^{10} + 522x^5 + 1 \\ C(x) = x^{11}-11x^6-x \end{gather*} are also related to the Belyi function of the icosidodecahedron (also $6912 = 4\cdot 12^3$): $$ F(z) = -6912 \frac{A(z)^3 C(z)^5}{B(z)^4}. $$ See the paper "Belyi functions for Archimedean solids" by Nicolas Magot and Alexander Zvonkin.
Mar 1, 2012 at 15:36 comment added Tito Piezas III Thanks so much, Prof. Elkies! I added a postscript to my original question giving the background why I asked about that particular surface.
Mar 1, 2012 at 14:28 vote accept Tito Piezas III
Mar 1, 2012 at 7:23 history edited Noam D. Elkies CC BY-SA 3.0
Correct sign error: consistency requires $-11x^6$, not $+11x^6$.
Mar 1, 2012 at 7:00 history answered Noam D. Elkies CC BY-SA 3.0