Visual symmetry is something that we detect effortlessly and seemingly instantaneously, giving it a special role in how we see the world. Although symmetry's most familiar role is in art, where it helps support aesthetic judgments, symmetry has a lesser-known but deeper role in everyday perception, where it supports object identification and categorization. But how flexible is human symmetry perception? Does it require an exact, geometric symmetry (as might be found in a scissor-cut paper doll) or a more qualitative or approximate symmetry based on a pattern of similar spatial relations (such as that of roughly-sketched stick figure)? We have been exploring this question in a study of how humans visually scan figures while judging symmetric and nearly-symmetric figures. When nearly-symmetric figures contained differences that broken the pattern of spatial relations, subjects spent less time examining them than when the differences were similar in magnitude, but did not break the pattern of spatial relations. This suggests that when we perceive symmetry, we are sensitive to not only the exact geometric symmetry but also the pattern of spatial relations, and that we notice these patterns very early, perhaps before the the very first eye movement. This is surprising, because sensitivity to patterns of relations was thought to be true only of slower and higher-level comparison processes such as analogy. This suggests that human symmetry perception is more powerful and flexible than was previously assumed, and may even have been an evolutionary precursor to higher-level comparison processes.