In this paper we propose an artificial intelligence imaging solution to support archaeologists in the classification task of Roman commonware potsherds. Usually, each potsherd is represented by its sectional profile as a two dimensional black-white image and printed in archaeological books related to specific archaeological excavations. The partiality and handcrafted variance of the fragments make their matching a challenging problem: we propose to pair similar profiles via the unsupervised hierarchical clustering of non-linear features learned in the latent space of a deep convolutional Variational Autoencoder (VAE) network. Our contribution also include the creation of a ROman COmmonware POTtery (ROCOPOT) database, with more than 4000 potsherds profiles extracted from 25 Roman pottery corpora, and a MATLAB GUI software for the easy inspection of shape similarities. Results are commented both from a mathematical and archaeological perspective so as to unlock new research directions in both communities.