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Recall that the icosahedron is the Platonic solid with 12 vertices and each face is an equilateral triangle. Let G denote the symmetry group of

Recall that the icosahedron is the Platonic solid with 12 vertices and each face is an equilateral triangle. Let G denote the symmetry group of (physically possible) symmetries of the icosahedron. Up to G-equivalence, how many ways are there to color the vertices of the icosahedron with two colors red and blue, so that exactly two vertices get colored red? 2

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