  A Delaunay polytope $P$ is said to be {\em extreme} if the only (up to
isometries) affine bijective transformations $f$ of $\R^n$, for which $f(P)$ is
again a Delaunay polytope, are the homotheties. This notion was introduced in
\cite{DGL92}; also some examples in dimension 1, 6, 7, 15, 16, 22, 23 were
constructed and it was proved that in dimension less than 6 there are no
extreme Delaunay polytopes, except the segment. In this note, for every $n\geq
6$ we build an extreme Delaunay polytope $ED_n$ of dimension $n$.
