  We construct three-qubit entanglement witnesses with the properties that all
the partial transposes have the spanning properties. These witnesses determine
faces for separable states whose interior lies in the interior of PPT states,
and so they detect sets of PPT entangled states with nonempty interiors. These
witnesses also detect all kinds of bi-separable pure product states. Our
construction depends on the observation that multi-partite entanglement
witnesses correspond to multi-linear maps which are positive.
