Construction of three-qubit biseparable states distinguishing kinds of entanglement in a partial separability classification

We construct seven kinds of three-qubit biseparable states to show that every class of biseparable states in the partial separability classification proposed by Szalay and K"ok'enyesi [S. Szalay and Z. K"ok'enyesi, Phys. Rev. A 86, 032341 (2012)] is nonempty.