According to Recognition-By-Components theory, object recognition relies on a specific subset of three-dimensional shapes called geons. In particular, these configurations constitute a powerful cue to three-dimensional object reconstruction because their two-dimensional projection remains viewpoint-invariant. While a large body of literature has demonstrated sensitivity to changes in these so-called nonaccidental configurations, it remains unclear what information is used in establishing such sensitivity. In this study, we explored the possibility that nonaccidental configurations can already be inferred from the basic constituents of objects, namely, their edges. We constructed a set of stimuli composed of two lines corresponding to various nonaccidental properties and configurations underlying the distinction between geons, including collinearity, alignment, curvature of contours, curvature of configuration axis, expansion, cotermination, and junction type. Using a simple visual search paradigm, we demonstrated that participants were faster at detecting targets that differed from distractors in a nonaccidental property than in a metric property. We also found that only some but not all of the observed sensitivity could have resulted from simple low-level properties of our stimuli. Given that such sensitivity emerged from a configuration of only two lines, our results support the view that nonaccidental configurations could be encoded throughout the visual processing hierarchy even in the absence of object context.