  We report here a computation giving the complete list of facets for the cut
polytopes over several very symmetric graphs with $15-30$ edges, including
$K_8$, $K_{3,3,3}$, $K_{1,4,4}$, $K_{5,5}$, some other $K_{l,m}$, $K_{1,l,m}$,
$Prism_7, APrism_6$, M\"{o}bius ladder $M_{14}$, Dodecahedron, Heawood and
Petersen graphs.
  For $K_8$, it shows that the huge lists of facets of the cut polytope
$CUTP_8$ and cut cone $CUT_8$, given in [CR] is complete. We also confirm the
conjecture that any facet of $CUTP_8$ is adjacent to a triangle facet.
  The lists of facets for $K_{1,l,m}$ with $(l,m)=(4,4),(3,5),(3,4)$ solve
problems (see, for example, [Werner]) in quantum information theory.
