AbstractManipulating wave propagation and energy collection plays a core role in modern physics, for which topological insulators hosting robust boundary states offer an ideal platform. However, there exist challenges in integrating multiple topological states like two-dimensional (2D) surface state, one-dimensional (1D) hinge state, and zero-dimensional (0D) corner state into a single three-dimensional (3D) architecture. Here we introduce a dimensional hierarchy acoustic structure with a piled 3D Kagome-chain crystal. By tuning the inter- and intra-layer hopping, we lift the 3D bulk states into 2D surface states. A further distortion on the in-plane unit cell makes the system support the 1D hinge and 0D corner states simultaneously. This hierarchy keeps the parent architecture unchanged. Analytically, we prove the robustness of our framework in different geometrical configurations. Our research offers insight for the practical use of the sonic or optical device with diversified topological modes like wave concentrations and transmissions.