  We construct a large class of indecomposable positive linear maps from the
$2\times 2$ matrix algebra into the $4\times 4$ matrix algebra, which generate
exposed extreme rays of the convex cone of all positive maps. We show that
extreme points of the dual faces for separable states arising from these maps
are parametrized by the Riemann sphere, and the convex hulls of the extreme
points arising from a circle parallel to the equator have the exactly same
properties with the convex hull of the trigonometric moment curve studied from
combinatorial topology. Any interior points of the dual faces are $2\otimes 4$
boundary separable states with full ranks. We exhibit concrete examples of such
states.
