Metonymies are known as ways of conceptualizing entities and situations of various sorts. For example, users of PCs usually call the icon depicting a waste paper basket 'basket'. They thus use the name of the depicted object for referring to the depicting object. We use a model airplane ("Baufix" airplane) as the paradigm case for investigating the semiotics of depictional metonymies and the role they are put to in construction dialogue. The airplane's structure is described in a GPSG format and given a model-theoretic semantics. We also describe how aggregates of the toy model are given depictional interpretations in the course of the construction dialogue. The coordinating role of metonymic language use is illustrated. It is also shown how cognition can be integrated into the model developed.