It has recently been shown that identical, isotropic particles can form complex crystals and quasicrystals. In order to understand the relation between the particle interaction and the structure, which it stabilizes, the phase behavior of a class of two-scale potentials is studied. In two dimensions, the phase diagram features many phases previously observed in experiment and simulation. The three-dimensional system includes the sigma phase with 30 particles per unit cell, not grown in simulations before, and an amorphous state, which we found impossible to crystallize in molecular dynamics. We suggest that the appearance of structural complexity in monodisperse systems is related to competing nearest neighbor distances and discuss implications of our result for the self-assembly of macromolecules.