The exploration of geometrical patterns stimulates the imagination and encourages abstract reasoning, which is a distinctive feature of human-level intelligence. In cognitive science, Gestalt principles such as symmetry have often explained significant aspects of human perception. We present a computational technique for building artificial intelligence (AI) agents that use symmetry as the organizing principle for addressing Dehaene’s test of geometric intelligence. Our work offers symmetry as a core principle for building AI agents capable of geometric intelligence and understanding Gestalt principles in human perception.