Amphiphilic invertible polymers (AIPs) are a new class of macromolecules that self-assemble into micellar structures and rapidly change structure in response to changes in solvent polarity. Using small-angle neutron scattering (SANS) data, we obtained a quantitative description of the invertible micellar assemblies (IMAs). The detailed composition and size of the assemblies (including the effect of temperature) were measured in aqueous and toluene polymer solutions. The results show that the invertible macromolecules self-assemble into cylindrical core-shell micellar structures. The composition of the IMAs in aqueous and toluene solutions was used to reveal the inversion mechanism by changing the polarity of the medium. Our experiments demonstrate that AIP unimers self-assemble into IMAs in aqueous solution, predominantly through interactions between the hydrophobic moieties of macromolecules. The hydrophobic effect (or solvophobic interaction) is the major driving force for self-assembly. When the polarity of the environment is changed from polar to nonpolar, poly(ethylene glycol) (PEG) and aliphatic dicarboxylic acid fragments of AIP macromolecules tend to replace each other in the core and the shell of the IMAs. However, neither the interior nor the exterior of the IMAs consists of fragments of a single component of the macromolecule. In aqueous solution, with the temperature increasing from 15 to 35 degrees C, the IMAs' mixed core from aliphatic dicarboxylic acid and PEG moieties and PEG-based shell change the structure. As a result of the progressive dehydration of the macromolecules, the hydration level (water content) in the micellar core decreases at 25 degrees C, followed by dehydrated PEG fragments entering the interior of the IMAs when the temperature increases to 35 degrees C.