The Convex Structure of the Set of N-Representable Reduced 2-Matrices

It is shown that in the finite-dimensional case the extreme points of the convex set of all N-representable 2-matrices D2 are exposed points and that for the case N = 3 and N = 4 the preimage of an exposed point under the contraction map is unique. In addition, the convex structure of both D2 and its associated polar is given in the case where the 1-rank is equal to N + 2. A long list of exposed points of D2 is given which includes all previously published examples as well as some new ones. However, this list is shown not to be exhaustive.