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. 
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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/

[1] A. A. Azamov, A. Sh. Kuchkarov, A. G. Holboyev, “The pursuitevasion game on the 1-skeleton graph of regular polyhedron. I”, Automation and Remote Control, 78:4 (2017), 754–761 | DOI | MR

[2] A. A. Azamov, A. Sh. Kuchkarov, A. G. Holboyev, “The pursuitevasion game on the 1-skeleton graph of regular polyhedron. II”, Automation and Remote Control, 78:10 (2018), 345–351 | MR

[3] A. A. Azamov, B. T. Samatov, $\Pi$-strategy. An elementary introduction to the theory of differential games, National University of Uzbekistan, Tashkent, 2000 | MR

[4] M. Berger, Geometry, v. 1, Springer-Verlag, Berlin, 1987 | MR

[5] H. S. M. Coxeter, Introduction to geometry, John Wiley and Sons, Inc, New York, 1961 | MR | Zbl

[6] J. Malkevitch, Shaping space: a polyhedral approach, eds. Senechal M., Flenk G., Birkhauser, Boston, 1988, 80–92 | MR

[7] L. A. Petrosjan, Differential games of pursuit, World Scientific Publisher, 1993 | MR