  State space structure of tripartite quantum systems is analyzed. In
particular, it has been shown that the set of states separable across all the
three bipartitions [say $\mathcal{B}^{int}(ABC)$] is a strict subset of the set
of states having positive partial transposition (PPT) across the three
bipartite cuts [say $\mathcal{P}^{int}(ABC)$] for all the tripartite Hilbert
spaces $\mathbb{C}_A^{d_1}\otimes\mathbb{C}_B^{d_2}\otimes\mathbb{C}_C^{d_3}$
with $\min\{d_1,d_2,d_3\}\ge2$. The claim is proved by constructing state
belonging to the set $\mathcal{P}^{int}(ABC)$ but not belonging to
$\mathcal{B}^{int}(ABC)$. For $(\mathbb{C}^{d})^{\otimes3}$ with $d\ge3$, the
construction follows from specific type of multipartite unextendible product
bases. However, such a construction is not possible for
$(\mathbb{C}^{2})^{\otimes3}$ since for any $n$ the bipartite system
$\mathbb{C}^2\otimes\mathbb{C}^n$ cannot have any unextendible product bases
[Phys. Rev. Lett. 82, 5385 (1999)]. For the $3$-qubit system we, therefore,
come up with a different construction.
