Teaching geometry courses for preservice elementary teachers, we observed that difficulty with classifying shapes (and, in particular, composite 3-D shapes) persists even after work with simple shapes to support the writing of accurate and unambiguous definitions. We conducted a self-study of our teaching of 3-D concepts to uncover the concept images of pyramid and prism that emerge. We sought to understand the nature of those observed difficulties. We found that using both simple and composite shapes in classification activity exposed more nuanced and complex concept imagery than simple shapes alone. Opportunities to articulate assumptions create a space for all learners to make the language more precise and to create concept definitions that are more resilient. [For the complete proceedings, see ED606531.]