On the Topology of the Double Staircase

This paper analyzes the double staircase from a topological point of view in three parts. First, it surveys historical archetypes of the double staircase, attending to their evolution and sundry topological varieties. Second, it presents a topological taxonomy for the double staircase which allows its rigorous formal classification. Third, it explores the generative range of algorithmically generated double staircases, particularly those derived directly from schematic circulation schemes. We introduce the medial axis as a technique uniquely suited to produce rich spatial models of double staircases from abstract topological diagrams. Through this investigation, we furnish a framework for the analysis and generation of models of the double staircase that embody various topological and spatial qualities. By interweaving historical taxonomies with contemporary practices of computational design, this study reintroduces the double staircase as an enduringly vital mode of architectural investigation.