Interchangeable components allow an object to be easily reconfigured but usually reveal that the object is composed of parts. In this work, we present a computational approach for the design of components which are interchangeable, but also form objects with a coherent appearance which conceals their composition from parts. These components allow a physical realization of Assembly Based Modelling, a popular virtual modelling paradigm in which new models are constructed from the parts of existing ones. Given a collection of 3D models and a segmentation that specifies the component connectivity, our approach generates the components by jointly deforming and partitioning the models. We determine the component boundaries by evolving a set of closed contours on the input models to maximize the contours’ geometric similarity. Next, we efficiently deform the input models to enforce both C0 and C1 continuity between components while minimizing deviation from their original appearance. The user can guide our deformation scheme to preserve desired features. We demonstrate our approach on several challenging examples, showing that our components can be physically reconfigured to assemble a large variety of coherent shapes.