 Solution

The Au(111) surface has three equivalent in-plane directions related by $120^{\circ }$ rotations. A reconstruction that contracts along only one direction creates anisotropic stress. Periodically changing boundary direction among equivalent orientations redistributes that strain and lowers its long-range elastic cost, while boundary formation and bending carry their own energy cost.

The resulting compromise produces the characteristic herringbone arrangement. Threefold symmetry explains the equivalent turning directions; a balance of elastic relaxation and boundary costs, rather than symmetry alone, sets the finite repeat distance.