  We propose a set of three simple photonic platforms capable of emulating
quantum topologically insulating phases corresponding to Hall, spin-Hall, and
valley-Hall effects. It is shown that an interface between any two of these
heterogeneous photonic topological insulators supports scattering-free surface
states. Spin and valley degrees of freedom characterizing such topologically
protected surface waves determine their unique pathways through complex
photonic circuits comprised of multiple heterogeneous interfaces.
