On strict suns in $\ell^\infty(3)$

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 $\ell^\infty(3)$.