Combinatorial computational geometry, while dealing with geometric objects as discrete entities, provides the means both to analyse and to construct relationships between these objects and relate them to other non-geometrical entities. This paper explores some ways in which this may be used in design through a review of six, one-semester-long design explorations by undergraduate and postgraduate students in the Flexible Modelling for Design and Prototyping course between 2004 and 2007. The course focuses on using computational geometry firstly to construct topologically defined design models based on graphs of relationships between objects (parametric design,) and concurrently to output physical prototypes from these “flexible models”(an application of numerical computational geometry). It supports students to make early design explorations. Many have built flexible models to explore design iterations for a static spatial outcome. Some have built models of real time responsive dynamic systems. In this educational context, computational geometry has enabled a range of design iterations that would have been challenging to uncover through physical analogue means alone. It has, perhaps more significantly, extended the students'own concept of the space in which they design.