Abstract:
It is considered a game between a group of $n$ pursuers and one evader moving with the same maximal speed along $1$-skeleton of a given regular polyhedron. In this paper it is considered the case of the regular polyhedrons with $24$ and $120$ vertices in the space $\mathbb{R}^4$. It is proven that if $n \leqslant 2$, then the evader wins in the game, and to the evader, if $n \geqslant 3$ then the game finishes successfully for the group of pursuers.