Self-assembly is a powerful technique for the bottom-up construction of discrete, well-defined nanoscale structures. Large multicomponent systems (with more than 50 components) offer mechanistic insights into biological assembly but present daunting synthetic challenges. Here we report the self-assembly of giant M24L48 coordination spheres from 24 palladium ions (M) and 48 curved bridging ligands (L). The structure of this multicomponent system is highly sensitive to the geometry of the bent ligands. Even a slight change in the ligand bend angle critically switches the final structure observed across the entire ensemble of building blocks between M24L48 and M12L24 coordination spheres. The amplification of this small initial difference into an incommensurable difference in the resultant structures is a key mark of emergent behavior.