The amorphization mechanism of icosahedral Pt nanoclusters is investigated by a combination of molecular dynamics simulations and density functional calculations. A general mechanism for amorphization, involving rosettelike structural transformations at fivefold vertices, is proposed. In the rosette, a fivefold vertex is transformed into a hexagonal ring. We show that, for icosahedral Pt nanoclusters, this transformation is associated with an energy gain, so that their most favorable structures have a low symmetry even at icosahedral magic numbers, and that the same mechanism underlies the formation of amorphous structures in gold.