Abstract 3D reconstruction of general scenes remains an open challenge with current techniques often reliant on assumptions on the scene’s surface reflectance, which restrict the range of objects that can be modelled. Helmholtz Stereopsis offers an appealing framework to make the modelling process agnostic to surface reflectance. However, previous formulations have been almost exclusively limited to 2.5D modelling. To address this gap, this paper introduces a family of reconstruction approaches that exploit Helmholtz reciprocity to produce complete 3D models of objects with arbitrary unknown reflectance. This includes an approach based on the fusion of (orthographic or perspective) view-dependent reconstructions, a volumetric approach optimising surface location within a voxel grid, and a mesh-based formulation optimising vertices positions of a given mesh topology. The contributed approaches are evaluated on synthetic and real datasets, including novel full 3D datasets publicly released with this paper, with experimental comparison against a wide range of competing methods. Results demonstrate the benefits of the different approaches and their abilities to achieve high quality full 3D reconstructions of complex objects.