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We report here a computation giving the complete list of facets for the cutpolytopes 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 andPetersen 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 theconjecture that any facet of $CUTP_8$ is adjacent to a triangle facet.  The lists of facets for $K_{1,l,m}$ with $(l,m)=(4,4),(3,5),(3,4)$ solveproblems (see, for example, [Werner]) in quantum information theory.

Enumeration of the facets of cut polytopes over some highly symmetric graphs