  In our previous works we have classified real non-singular cubic
hypersurfaces in the 5-dimensional projective space up to equivalence that
includes both real projective transformations and continuous variations of
coefficients preserving the hypersurface non-singular. Here, we perform a finer
classification giving a full answer to the chirality problem: which of real
non-singular cubic hypersurfaces can not be continuously deformed to their
mirror reflection.
