In this work, we study optical properties of an array of dielectric periodic waveguides that possess two modes with identical frequencies and wavenumbers and characterized by the different symmetry with respect to the plane that contains the waveguide axis. Due to the presence of two modes, the field pattern of the wave excited in an individual waveguide can be highly asymmetric. We demonstrate that such a feature leads to the opening of the topological bandgap in the dispersion of the infinite array of equidistantly spaced identical two-mode waveguides. In agreement with the bulk-edge correspondence, the finite array of the waveguides supports two topological edge modes, regardless of the number of the waveguides in the array.

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