of a dodecahedron in 3-space, so there is a representation A₅ -> SO₃('''R''').

In this picture the vertices of the polyhedra represent the elements of the group, with the center of the sphere representing the identity element. Each vertex represents a rotation about the axis pointing from the center to that vertex, by an angle equal to the distance from the origin, in radians. Vertices in the same polyhedron are in the same conjugacy class. Since the conjugacy class equation for A₅ is 1=1 + 12 + 12 + 15