The extreme rays of the 6x6 copositive cone

We provide a complete classification of the extreme rays of the 6×6 copositive cone C6.  We proceed via a coarse intermediate classification of the possible minimal zero support set of an exceptional extremal matrix A∈C6.  To each such minimal zero support set, we construct a union of manifolds in the space of real symmetric 6×6 matrices S6,  parameterized in a semi-trigonometric way, which consists of all exceptional extremal matrices A in C6 having this minimal zero support set.
Joint work with Roland Hildebrand, Univ. Grenoble Alpes, CNRS and Peter J.C. Dickin-son, RaboBank.