  A graph G is prismatic if for every triangle T of G, every vertex of G not in
T has a unique neighbour in T. The complement of a prismatic graph is called
\emph{antiprismatic}. The complexity of colouring antiprismatic graphs is still
unknown. Equivalently, the complexity of the clique cover problem in prismatic
graphs is not known.
  Chudnovsky and Seymour gave a full structural description of prismatic
graphs. They showed that the class can be divided into two subclasses: the
orientable prismatic graphs, and the non-orientable prismatic graphs. We give a
polynomial time algorithm that solves the clique cover problem in every
non-orientable prismatic graph. It relies on the the structural description and
on later work of Javadi and Hajebi. We give a polynomial time algorithm which
solves the vertex-disjoint triangles problem for every prismatic graph. It does
not rely on the structural description.
