[en] Working within the covariant formalism, we construct a 3-string vertex for closed bosonic strings compactified on M x Ω, where M is a (26-2d)-dimensional Minkowski space and Ω is a d-complex dimensional orbifold obtained by quotienting a torus. Starting from an overlap that describes the splitting and joining of 3 twisted strings, we obtain a well defined expression for the vertex in an oscillator basis, using matching conditions on the strings. The consistency of the vertex in this basis is demonstrated by proving that it satisfies various Goto-Naka-type continuity conditions. (orig.)