  Jakobson and Nadirashvili \cite{JN} constructed a sequence of eigenfunctions
on $T^2$ with a bounded number of critical points, answering in the negative
the question raised by Yau \cite{Yau1} which asks that whether the number of
the critical points of eigenfunctions for the Laplacian increases with the
corresponding eigenvalues.
  The present paper finds three interesting eigenfunctions on the minimal
isoparametric hypersurface $M^n$ in $S^{n+1}(1)$. The corresponding eigenvalues
are $n$, $2n$ and $3n$, while their critical sets consist of $8$ points, a
submanifold(infinite many points) and $8$ points, respectively. On one of its
focal submanifolds, a similar phenomenon occurs.
