  We analyze the facial structures of the convex set consisting of all two
qubit separable states. One of faces is a four dimensional convex body
generated by the trigonometric moment curve arising from polyhedral
combinatorics. Another one is an eight dimensional convex body, which is the
convex hull of a homeomorphic image of the two dimensional sphere. Extreme
points consist of points on the surface, and any two of them determines an
edge. We also reconstruct the trigonometric moment curve in any even
dimensional affine space using the qubit-qudit systems, and characterize the
facial structures of the convex hull.
