Calix[4]arene-derived surfactants form monodisperse micelles with a well-defined aggregation number (Nagg ) of 4, 6, 8, 12, or 20, corresponding to the Platonic solids. This feature is in strong contrast to conventional micelles. In this study, a transition from a dodecamer (Nagg =12) to an icosamer (Nagg =20) was induced by a rapid increase in the NaCl concentration (CNaCl ) using a stopped-flow device and directly observed by time-resolved small-angle X-ray scattering. The Nagg remained unchanged during the first 60 s after the increase in CNaCl , and then abruptly increased to 20. This feature resembles phase transitions in supersaturated or supercooled states, or highly cooperative phenomena. We surmise that this finding may be due to the fact that only a few Nagg values are thermodynamically allowed when Nagg is sufficiently small. This is the first observation of such an induction time in micellar aggregation.