Making sense of complex objects is difficult, and typically requires the use of external representations to support cognitive demands while reasoning about the objects. Visualizations are one type of external representation that can be used to support sensemaking activities. In this paper, we investigate the role of two design strategies in making the interactive features of visualizations more supportive of users’ exploratory needs when trying to make sense of complex objects. These two strategies are visibility and complementarity of interactions. We employ a theoretical framework concerned with human–information interaction and complex cognitive activities to inform, contextualize, and interpret the effects of the design strategies. The two strategies are incorporated in the design of Polyvise, a visualization tool that supports making sense of complex four-dimensional geometric objects. A mixed-methods study was conducted to evaluate the design strategies and the overall usability of Polyvise. We report the findings of the study, discuss some implications for the design of visualization tools that support sensemaking of complex objects, and propose five design guidelines. We anticipate that our results are transferrable to other contexts, and that these two design strategies can be used broadly in visualization tools intended to support activities with complex objects and information spaces.