  Let H[N] denote the tensor product of n finite dimensional Hilbert spaces
H(r). A state |phi> of H[N] is separable if |phi> is the tensor product of
states in the respective product spaces. An orthogonal unextendible product
basis is a finite set B of separable orthonormal states |phi(k)> such that the
non-empty space B9perp), the set of vectors orthogonal to B, contains no
separable projection. Examples of orthogonal UPB sets were first constructed by
Bennett et al [1] and other examples appear, for example, in [2] and [3]. If F
denotes the set of convex combinations of the projections |phi(k)><phi(k)|,
then F is a face in the set S of separable densities. In this note we show how
to use F to construct families of positive partial transform states (PPT) which
are not separable. We also show how to make an analogous construction when the
condition of orthogonality is dropped. The analysis is motivated by the
geometry of the faces of the separable states and leads to a natural
construction of entanglement witnesses separating the inseparable PPT states
from S.
