Abstract <p>Additive manufacturing (AM) processes rely heavily on the geometric intricacies of parts being produced. Variations in the geometry of sequentially printed layers can introduce defects, arising from the complex interactions between geometry, process parameters, and materials. To mitigate these errors, it is critical to identify key geometric features and track their evolution in terms of both location and timing throughout the design and manufac- turing stages. This paper presents a novel method to describe shape in the context of AM, emphasizing the importance of layer-wise material deposition. Mereotopology, a framework for qualitatively describing the relationships between parts and wholes, is employed to pro- vide insights into the spatial, temporal, and spatio-temporal relationships inherent in AM processes. This formalism is particularly suited for shapes where precise dimensions may be indeterminate but where relational descriptions can still offer valuable information. The proposed theory integrates spatio-temporal evolution based on mereotopological principles and is applied to benchmark cases in AM. Additionally, a methodology for visualizing the generated descriptions is provided, along with a detailed case study. The paper concludes with a discussion on the strengths and limitations of this theory in comparison to existing approaches for describing four-dimensional objects.</p> Graphical abstract <p></p>