Polyhedral structures are a fascinating and efficient case of structural virtuosity. However, their adoption to date has been limited because of geometrical, structural and fabrication complexities. This paper introduces a modelling pipeline to provide a rigorous -yet practical-approach to the challenges linked to the realisation of 3D polyhedral structures, from early-stage design to fabrication. A custom-developed modelling add-on is utilised for reconstructing the underlying topology of 3D polyhedral structures and implementing a component-based approach for the design development. Concurrently, an innovative digital fabrication strategy based on Additive Formwork Manufacturing is presented, with a detailed description of the process and illustration of a fully-functional physical prototype. Methodological and software developments are applied to the fabrication experiments where the approach is tested with in-depth design and construction insights. The approach is ultimately discussed for the development of real-world structures and in light of the potential adoption by non-expert computational designers.