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I have two questions about the class of integer-coefficient polynomials all of whose roots are rational. I asked this at MSE, but it attracted little interest (perhaps because it is not interesting!) ...

$$1728 V^5 + F^3 = E^2 \;.$$ Can anyone point me to a concise, modern derivation and explanation of the significance of the icosahedron equation, more modern and concise than Klein's description in ...