Crafting crystalline topological insulators via accidental mode degeneracies

Crystalline topological insulators have recently become a powerful platform for realizing photonic topological states from microwaves to the visible. Appropriate geometric symmetries of the lattice are at the core of their functionality. Here we put forward an alternative approach to craft those systems by designing the internal symmetries of the Hamiltonian via accidental mode degeneracies. We illustrate our approach constructing an analog of breathing honeycomb lattice using simpler lattice geometry and six times less meta-atoms, revealing edge and corner states, and calculating the relevant topological invariants.