Law of structure for the 1:2:3 resonant chain. The left (right) column of panels show the relation between the mean motion ratio n₁/n₂ (n₂/n₃) and the eccentricities (e₁, e₂, e₃ from top to bottom). Blue lines are for the stable symmetric ACR families (S₆) while the black lines for the stable asymmetric family (A₆). On each panel, the lowest line is for the planets in the Kepler-51 system, while the middle and the top lines are for the cases of 10 and 100 times more massive planets, respectively (see text). The critical points, at which the S₆ family becomes unstable and the asymmetric solution appears, are denoted by red crosses.