This paper deals with the design of interactivity in visualization tools. There are several factors that can be used to guide the analysis and design of the interactivity of these tools. One such factor is flow, which is concerned with the duration of interaction with visual representations of information--interaction being the actions performed by users on these representations and the reactions given back by the representations. Four forms of flow can be identified: 1) continuous action, continuous reaction; 2) continuous action, discrete reaction; 3) discrete action, continuous reaction; and 4) discrete action, discrete reaction. Structuring micro-level interactions of tools based on these forms of flow can have varying effects on the cognitive processes of users. Based on this classification of flow, four versions of an interactive visualization tool were created and studied. The testbed for this study was 3D geometric solids--more specifically, Platonic and Archimedean solids. A multi-method empirical study was conducted to evaluate the usability of these four interfaces and their effect on learning, visual thinking, and exploration. This paper reports some findings of this study. (Contains 14 figures, 9 tables, and 3 footnotes.)