A load-carrying modular structure assembled from 3-D structural modules constituting parallelepipeds with rectangular faces, the 3-D modules adjoining each other along said faces. The modules comprise reinforcing diagonal beams (RDBs) disposed along diagonals that connect vertices of the parallelepipeds. The RDBs form a 3-D multi-tetrahedron lattice whereby said modular structure behaves under load as a multi-tetrahedron structure. A basic 3-D module for assembling the modular structure has six RDBs along facial diagonals forming a tetrahedron. The 3-D module may have RDBs also along the other six diagonals and along diagonals connecting centers of the box's faces. The 3-D modules may have cut-outs and passages for water currents. They may have internal hollow volumes and controlled buoyancy, and may be assembled from shell elements.