  The lists of facets -- $298,592$ in $86$ orbits -- and of extreme rays --
$242,695,427$ in $9,003$ orbits -- of the hypermetric cone $HYP_8$ are
computed. The first generalization considered is the hypermetric polytope
$HYPP_n$ for which we give general algorithms and a description for $n\le 8$.
Then we shortly consider generalizations to simplices of volume higher than
$1$, hypermetric on graphs and infinite dimensional hypermetrics.
