The goal of this study was to characterise how third-grade primary school students understand the concept of polygon as well as relationships between polygons. Following a teaching experiment, students answered a questionnaire on the recognition of polygons and relationships between polygons, providing information about how a polygon was understood as an example of a class. Dimensional deconstruction of shapes (Duval, 2017) and "Statistical Implicative Analysis" (Gras, Suzuki, Guillet, & Spagnolo, 2008) were used to analyse students' answers. The findings indicated that students' understanding of the polygon concept depended on how students recognised and modified the relevant attributes considered in the definition of polygon. These results suggest that a progressive complexity underlies the understanding of the concept of polygon. Evidence of this progressive complexity was found in the relationship between recognising a figure as a polygon and transforming a non-example of a polygon into a polygon. Furthermore, the ability to identify a polygon as an instance of a class depended on the attribute that defines the class. That is, the fact of identifying a class of polygons was linked to the non-relevant attribute considered. Instructional implications are finally drawn regarding the key role of dimensional deconstruction to understand polygons and relationships between polygons.