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Higher-order topological insulators^{, , , –} are a family of recently predicted topological phases of matter that obey an extended topological bulk–boundary correspondence principle. For example, a two-dimensional (2D) second-order topological insulator does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D topological insulator, but instead has topologically protected zero-dimensional (0D) corner states. The first prediction of a second-order topological insulator, based on quantized quadrupole polarization, was demonstrated in classical mechanical and electromagnetic^, metamaterials. Here we experimentally realize a second-order topological insulator in an acoustic metamaterial, based on a ‘breathing’ kagome lattice that has zero quadrupole polarization but a non-trivial bulk topology characterized by quantized Wannier centres^,,. Unlike previous higher-order topological …