Weyl semimetals and higher-order topological phases represent two fundamental yet distinct classes of topological matter. While both have been extensively studied in classical-wave systems, their coexistence and controllable transition remain largely unexplored. Meanwhile, emulating three-dimensional spin-orbit couplings, which are crucial for realizing a broad class of higher-dimensional synthetic topological phases, continues to pose significant experimental challenges. Here, we experimentally emulate three-dimensional spin–orbit coupling in a circuit metamaterial and show that tuning the coupling strength into a dimerized configuration enables the coexistence of and a controllable transition between a Weyl semimetal phase and a third-order topological insulator phase. We observe hallmark signatures of both phases, including Fermi arcs revealed by frequency-resolved spectroscopy and topological corner modes probed via local density-of-states measurements. Interestingly, the corner mode degeneracy doubles compared to that in the canonical Benalcazar-Bernevig-Hughes model, signaling an enriched topological structure. Our study establishes a fundamental connection between two paradigmatic topological phases and paves the way for further exploring spin-orbit-coupling-induced exotic higher-dimensional topological phases.

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• Spin-orbit coupling
• Topolectrical circuits
• Topological effects in acoustic systems
• Topological effects in photonic systems
• Topological phases of matter