Aerosol-OT (AOT) reverse micelles are a well-known, self-assembled model system for studying water in nanoconfinement. Although all-atom molecular dynamics (MD) simulations universally find AOT reverse micelles to be non-spherical, most theories about the reverse micelles still assume a spherical shape for simplicity, such as the core/shell hypothesis. This simplification ignores any interactions between the shape of the self-assembled reverse micelle and the water or solutes confined within. I have developed a system of metrics that allows quantitative and independently-meaningful characterization of arbitrary, non-spherical shapes, like those of reverse micelles. These metrics include coordinate-pair eccentricity, which measures the overall distribution of mass in the shape; convexity, which provides a compact measure of the imperfections of the shape; and the curvature distribution, which directly reports how the surface curves. I apply these metrics to set of different MD parameterizations for AOT reverse micelles to uncover which factors contribute most to the observed shape and behavior. Despite the complexity of fluctuations of an amorphous shape, our metrics have allowed us to identify several fundamental behaviors and properties not previously reported in the reverse micelles.