摘要：The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological ***,we report three-dimensional(3D)wave-steering capabilities enabled by topological boundary states at three different orders in a 3D phononic crystal with nontrivial bulk topology originated from the synergy of mirror symmetry of the unit cell and a non-symmorphic glide symmetry of the *** multitude of topological states brings diverse possibilities of wave *** judicious engineering of the boundary modes,we experimentally demonstrate two functionalities at different dimensions:2D negative refraction of sound wave enabled by a firstorder topological surface state with negative dispersion,and a 3D acoustic interferometer leveraging on second-order topological hinge *** work showcases that topological modes at different orders promise diverse wave steering applications across different dimensions.