We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation ${\mathcal{E}}_{i|jk}^{\alpha }\le {\mathcal{E}}_{j|ik}^{\alpha }+{\mathcal{E}}_{k|ij}^{\alpha }$ holds for all subadditive bipartite entanglement measure $\mathcal{E}$, all permutations under parties $i,j,k$, all $\alpha \in [0,1]$, and all pure tripartite states. Then, we rigorously prove that the nonobtuse triangle area, enclosed by side ${\mathcal{E}}^{\alpha }$ with $0<\alpha \le 1/2$, is a measure for genuine tripartite entanglement. Finally, it is significantly strengthened for qubits that given a set of subadditive and nonsubadditive measures, some state is always found to violate the triangle relation for any $\alpha >1$, and the triangle area is not a measure for any $\alpha >1/2$. Our results pave the way to study discrete and continuous multipartite entanglement within a unified framework.

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• Entanglement measures
• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Resource theories