Considering {0, 1, ∞} as the vertices of a triangle, and the anharmonic group as its stabilizer, the fixed points of the 2-cycles are the points {−1, 1/2, 2}, which correspond to the midpoints of the edges (and the 2-cycles as rotation about that edge), and the fixed points of the 3-cycles are ${\displaystyle e^{\pm i\pi /3}}$, which correspond to the top and bottom poles (centers of the sides; the 3-cycles correspond to rotation through their axis), and are interchanged by the 2-cycles.

${\displaystyle e^{-i\pi /3}}$