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Degenerate bound states in the continuum in square and triangular open acoustic resonators

We consider square and equilateral triangular open acoustic resonators with the $C_{4v}$ and $C_{3v}$ symmetries, respectively. There is an unique property of square and triangular resonators of accidental number four-fold degeneracy of eigenstates that gives rise to two-fold degenerate Friedrich-Wintgen (FW) BICs. Compared to usual FW BICs the degenerate FW BICs maintain high $Q$-factor in wide range of the size of resonators. That removes the fabrication difficulties of proper choice of resonator. The presence of degenerate BICs in triangular resonators is extremely sensitive to switch output flows by small perturbations with $100\%$ efficiency.