Design entails the interaction of minds and the tools used to express the design, notably, diagrams. Systems designers use the affordances of the page when they generate structural diagrams of systems. Specifically, they use proximity to augment connectedness (path) information by grouping subsystems. They use horizontal position on the page to express sequence and vertical position to reflect actual spatial position. Finally, they use the permanence of diagrams to generate alternative designs. These conclusions were reached through the analysis of work by student designers, many of whom were practicing information technology professionals. The analysis of designs in topological and Euclidean space required the creation of computational tools that show promise as decision aids for designers, by separating the intertwined qualities of topological and Euclidean space, and by making visible the conceptual similarity of design alternatives.