  We construct faces of the convex set of all $2\otimes 4$ bipartite separable
states, which are affinely isomorphic to the simplex $\Delta_{9}$ with ten
extreme points. Every interior point of these faces is a separable state which
has a unique decomposition into 10 product states, even though ranks of the
state and its partial transpose are 5 and 7, respectively. We also note that
the number 10 is greater than $2\times 4$, to disprove a conjecture on the
lengths of qubit-qudit separable states. This face is inscribed in the
corresponding face of the convex set of all PPT states so that sub-simplices
$\Delta_k$ of $\Delta_{9}$ share the boundary if and only if $k\le 5$. This
enables us to find a large class of $2\otimes 4$ PPT entangled edge states with
rank five.
