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In a recent study by Xie and Eberly [Phys. Rev. Lett. 127, 040403 (2021)], anovel geometric measure of genuine tripartite entanglement was introduced.Although various extensions of this measure to four qubits have been proposed,they are not without limitations. In this work, we present a new extension ofthis geometric measure to four qubits based on a tetrahedron construction. Weuse the new measure to compare the entanglement ranking between two highlyentangled four-qubit states. We also discuss future avenues for furthergeneralizations along this geometric path.

Unraveling the Mysteries of Multipartite Entanglement: A Journey Through Geometry