American Mathematical SocietyFigure 1. When the Brioschi parameter loops around $B=0$ along the blue loop $\sigma$ as shown on the left, the roots undergo the cyclic permutation $(14352)$ as shown on the right. In a similar way, when $B$ loops around $B=-1/1728$ along the red loop $\gamma$, the roots undergo the cyclic permutation $(153)$. These permutations generate $A_5$. Enter the Icosahedron Now for a wonderful fact: we w
