  A subset M of a normed linear space X is said to be a {\it strict sun} if,
for every point $x\in X\setminus M$, the set of its nearest points from~$M$ is
non-empty and if $y\in M$ is a nearest point from M to x, then y is a nearest
point from M to all points from the ray $\{\lambda x+(1- \lambda)y |
\lambda>0\}$. In the paper there obtained a geometrical characterisation of
strict suns in $\ell^\infty(3)$.
