The directed migration of epithelial cell collectives through coordinated movements is key to many physiological and pathological processes and is increasingly well understood at the level of large confluent monolayers. Numerous migration processes rely on the migration of small groups of polarized epithelial clusters and their responses to external geometries. However, the interplay of cell-cell interactions and external boundaries in small cell clusters remain poorly understood. To tackle this, we used micropatterned stripes to investigate the migration of small epithelial clusters with well-defined geometries. Here we show that their migration efficiency is strongly dependent on the contact geometry, and in particular whether cell-cell contacts are parallel or perpendicular to the direction of migration. By systematically screening possible interaction mechanisms in a minimal active matter model, we show that a combination of velocity and polarity alignment with contact inhibition of locomotion captures the experimental data, which we then validated via force and intracellular stress measurements, as well as perturbations. Altogether, our results highlight the importance of geometry in defining the migration properties of cell clusters, providing a conceptual framework to extract interaction rules from how active systems interact with physical boundaries.