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Using extensive, unbiased searches based on density-functional theory, we explore the structural evolution of Cu n clusters over the size range n= 8–20⁠. For n= 8–16⁠, the optimal structures are plateletlike, consisting of two layers, with the atoms in each layer forming a trigonal bonding network similar to that found in smaller, planar clusters (n⩽ 6)⁠. For n= 17 and beyond, there is a transition to compact structures containing an icosahedral 13-atom core. The calculated ground-state structures are significantly different from those predicted earlier in studies based on empirical and semiempirical potentials. The evolution of the structure and shape of the preferred configuration of Cu n⁠, n⩽ 20⁠, is shown to be nearly identical to that found for Na clusters, indicating a shell-model-type behavior in this size range.