<p>This paper investigates polyhedral geometry as a pedagogical framework for integrating parametric modeling and digital fabrication in architectural education. Although computational tools enable formal complexity, they often insufficiently connect geometric reasoning with material and fabrication constraints. Addressing this gap, the study presents a design-based teaching approach centered on lamp design using Platonic and Archimedean solids as generative systems. Students developed parametric models in Rhino3D-Grasshopper and fabricated full-scale prototypes through digital and analog processes. Emphasis was placed on digital-to-physical workflows, geometric logic, material behavior, and joinery. While limited to a single course and design typology, the study shows how geometry-driven fabrication can strengthen critical understanding of constructability.</p>