  Roughly speaking, the rank of a Delaunay polytope (first introduced in
\cite{DGL92}) is its number of degrees of freedom. In \cite{DL}, a method for
computing the rank of a Delaunay polytope $P$ using the hypermetrics related to
$P$ is given. Here a simpler more efficient method, which uses affine
dependencies instead of hypermetrics is given. This method is applied to
classical Delaunay polytopes.
  Then, we give an example of a Delaunay polytope, which does not have any
affine basis.
