Topological waveguides with arbitrary pathway are desirable for many applications. In this paper we construct a triangular compound lattice consisting of magnetic dielectric rods. By breaking the space symmetry and the time-reversal symmetry, the structure generates topological edge states from the hybrid quantum Hall effects and valley Hall effects. This topological edge waveguide pathway can be arbitrary arranged just by the external magnetic field. The hybrid topological phase provides a new and ultraflexible way to the reconfiguration of the topological edge states.

In this paper, we have constructed a compound triangular lattice in which the optical quantum spin Hall effects and quantum valley Hall effects can simultaneously occur. Through the rotation of the dielectric rods in the lattice, two complete photonic band gaps with nontrivial topology can be created, one of which is due to the band inversion associated with the pseudospin degree of freedom at point in the first Brillouin zone (BZ) and the other due to the gapping out of Dirac cones associated with the valley degree of freedom at K point in the first BZ. The transformation between the two kinds of topological edge states can be also achieved through the rotation of the dielectric rods. A four-channel structure model is proposed to demonstrate the transformation and to achieve the channel switch of the topological edge states.