Ultrathin sheets of transition metal dichalcogenides (MX 2 ) with charge density waves (cDWs) is increasingly gaining interest as a promising candidate for graphene-like devices. Although experimental data including stripe/quasi-stripe structure and hidden states have been reported, the ground state of ultrathin MX 2 compounds and, in particular, the origin of anisotropic (stripe and quasi-stripe) cDW phases is a long-standing problem. Anisotropic cDW phases have been explained by coulomb interaction between domain walls and inter-layer interaction. However, these models assume that anisotropic domain walls can exist in the first place. Here, we report that anisotropic CDW domain walls can appear naturally without assuming anisotropic interactions: We explain the origin of these phases by topological defect theory (line defects in a two-dimensional plane) and interference between harmonics of macroscopic cDW wave functions. We revisit the McMillan-nakanishi-Shiba model for monolayer 1T-taS 2 and 2H-taSe 2 and show that CDWs with wave vectors that are separated by 120° (i.e. the three-fold rotation symmetry of the underlying lattice) contain a free-energy landscape with many local minima. Then, we remove this 120° constraint and show that free energy local minima corresponding to the stripe and quasi-stripe phases appear. our results imply that coulomb interaction between domain walls and inter-layer interaction may be secondary factors for the appearance of stripe and quasi-stripe CDW phases. Furthermore, this model explains our recent experimental result (appearance of the quasi-stripe structure in monolayer 1T-taS 2 ) and can predict new CDW phases, hence it may become the basis to study cDW further. We anticipate our results to be a starting point for further study in two-dimensional physics, such as explanation of "Hidden CDW states", study the interplay between supersolid symmetry and lattice symmetry, and application to other van der Waals structures.Usually, anisotropic structures such as stripe phases can be explained by anisotropic interaction between the constituent atoms, electrons, or liquid crystal polymers 1 . Anisotropic structures in charge density waves (CDWs) have been explained likewise. CDWs are periodic modulations of electric charge density in low-dimensional conductors 2-6 . The stability of CDWs containing stripe domain walls 7,8 was first studied by free energy theories 9,10 . But these theories assumed that stripe domain walls can exist in the first place, probably due to weak computational facilities at that time. The appearance of stripe domain walls and quasi-stripe (triclinic) domain walls 8,11,12 has been explained by Coulomb interaction between domain walls 13 and three-dimensional stacking 14 . However, are these interactions indispensable? It would be ideal to have rich structures with the least amount of interactions.In this article we report that stripe and quasi-stripe CDW domain walls can appear without anisotropic interactions and explain the origin of these phases by topolo...