Three-dimensional magic angles enabled with an acoustic metacube

Hyperbolic moiré materials enable exotic band hybridization, flat-band physics and magic angles1-4, but have so far been mostly restricted in two dimensions5-7. Here we introduce a nonlocal acoustic metacube architecture that lifts these intrinsic constraints and powers up a genuinely three-dimensional (3D) regime of moiré band engineering. In this 3D setting, the magic angle concept is generalized through the inequivalence of eigen-dispersion projections along three mutually orthogonal directions, enabling rich multidirectional band hybridizations that cannot occur in planar systems. As a result, the metacube stably supports multidimensional dispersion reconfiguration, flat-band formation, and asymmetric wave transport, while allowing wave propagation beyond surface confinement with pronounced out-of-plane radiation. By establishing a reconfigurable 3D nonlocal framework for moiré physics, this work defines a new regime of high-dimensional band hybridization and wave control.