Dirac cones and higher-order topology in quasi-continuous media

We consider the Dirac cones and higher-order topological phases in quasi-continuous media of classical waves (e.g., photonic sonic crystals). Using crystals as prototype examples, we revisit some known systems study acoustics. show emergence various band gaps same motherboard by tuning geometry system. provide a pedagogical review underlying physics methodology via bulk-edge-corner correspondence, symmetry-based indicators, Wannier representations, filling anomaly, fractional corner charges. In particular, theory topology are put framework. These examples principles can be inspiring useful future metamaterials.