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Crystalline topological insulators have recently become a powerful platformfor realizing photonic topological states from microwaves to the visible.Appropriate geometric symmetries of the lattice are at the core of theirfunctionality. Here we put forward an alternative approach to craft thosesystems by designing the internal symmetries of the Hamiltonian via accidentalmode degeneracies. We illustrate our approach constructing ananalog ofbreathing honeycomb lattice using simpler lattice geometry and six times lessmeta-atoms, reveal edge and corner states and calculate the relevanttopological invariants.

Crafting crystalline topological insulators via accidental mode degeneracies