Machine learning is a useful way of identifying representative or pure nanoparticle shapes as part of a larger ensemble, but its predictive capabilities can be limited when a large dataset of candidate structures must already exist. Ideally one would like to use machine learning to define the ideal dataset for future, more computationally intensive, studies before a significant amount of resources are consumed. In this work we combine an established analytical phenomenological model and statistical machine learning to predict the archetypes and prototypes of a diverse ensemble of 2380 platinum nanoparticle morphologies developed with less than twenty input electronic structure simulations. By parameterising a size- and shape-dependent thermodynamic model, probabilities are assigned to seventeen different shapes between three and thirty nanometres, which together with structural features such as nanoparticle diameter, surface area, sphericity and facet configuration form the basis for archetypal analysis and K-means clustering. Using this approach we rapidly identify six "pure" archetypes and twelve "representative" prototypes that can be used in future computational studies of properties such as catalysis.