This project introduces an approach to the computational design and fabrication of complex polyhedral structures that takes advantage of both parametric flexibility and modular logic, and is suitable for rapid prototyping. The methods presented codify material, geometric, and mechanical constraints in a flexible language of design components that forms the basis of a generalizable material and device- specific design system. Extending the geometric and tectonic possibilities of flat- cut assemblies, our approach resolves local deformations through an adaptive joint design, and facilitates processes of bottom-up design exploration which advance in parallel with their tectonic resolution. We illustrate our approach by documenting the system’s computational and material logic, a series of prototypes, and a full- scale installation based on the Wearie- Phelan structure, an aperiodic space-filling geometric construct that approximates the geometry of foam.