The emerging $\mathbb{Z}$-classified higher-order topological insulators (HOTIs), featuring multiple topological corner states per site, have attracted extensive interest due to their multipole chiral number (MCN) protection and potential for quantum-inspired device engineering. While 2D HOTIs with $\mathrm{MCN}>1$ have been demonstrated on classical platforms, 3D realizations have remained experimentally elusive primarily due to stringent long-range hopping requirements. Here, we present the first experimental realization of 3D $\mathbb{Z}$-classified HOTIs with large MCNs by implementing a synthetic orbital approach through a 3D Su-Schrieffer-Heeger model incorporating degenerate $p$ orbitals. By explicitly incorporating orbital degrees of freedom into the HOTI design, our work enables multidimensional wave control while circumventing conventional hopping limitations. This demonstration of the orbital-engineering paradigm establishes a versatile platform for developing highly integrated acoustic devices.

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• Acoustic metamaterials
• Topological effects in acoustic systems
• Topological insulators