Geodesic
The pursuit-evasion game on the $1$-skeleton graph of the regular polyhedron.~III
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 4, pp. 5-23

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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.
Keywords: pursuit-evasion game, approach problem, evasion problem, positional strategy, counter strategy, exact catch, regular polyhedron with $24$ vertices, regular polyhedron with $120$ vertices, one-dimensional graph. 
@article{MGTA_2019_11_4_a1,
     author = {Abdulla A. Azamov and Atamurat Sh. Kuchkarov and Azamat G. Holboyev},
     title = {The pursuit-evasion game on the $1$-skeleton graph of the regular {polyhedron.~III}},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {5--23},
     publisher = {mathdoc},
     volume = {11},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2019_11_4_a1/}
}
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Abdulla A. Azamov; Atamurat Sh. Kuchkarov; Azamat G. Holboyev. The pursuit-evasion game on the $1$-skeleton graph of the regular polyhedron.~III. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 11 (2019) no. 4, pp. 5-23. http://geodesic.mathdoc.fr/item/MGTA_2019_11_4_a1/