This is a companion paper of a previous work on the surface reconstruction from a sparse cloud of points, which are estimated by Structure-from-Motion. The surface is a 2-manifold sub-complex of the 3D Delaunay triangulation of the points. It is computed as the boundary of a list of tetrahedra, which grows in the set of Delaunay tetrahedra. Here we detail the proofs for the 2-manifold tests that are used during the growing: we show that the tetrahedron-based test and the test for adding (or subtracting) one tetrahedron to (or from) the list are equivalent to standard tests based on triangles.