Geodesic
A necessary and sufficient condition for the existence of simple closed geodesics on regular tetrahedra in spherical space
Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 161-172 Cet article a éte moissonné depuis la source Math-Net.Ru

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A necessary and sufficient condition is obtained for the existence of a simple closed geodesic of type $(p,q)$ on a regular tetrahedron in spherical space. Bibliography: 6 titles.
Keywords: simple closed geodesics, regular tetrahedron, spherical space, Lobachevsky space. 
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A. A. Borisenko. A necessary and sufficient condition for the existence of simple closed geodesics on regular tetrahedra in spherical space. Sbornik. Mathematics, Tome 213 (2022) no. 2, pp. 161-172. http://geodesic.mathdoc.fr/item/SM_2022_213_2_a1/

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[2] D. B. Fuchs, E. Fuchs, “Closed geodesics on regular polyhedra”, Mosc. Math. J., 7:2 (2007), 265–279 | DOI | MR | Zbl

[3] V. Yu. Protasov, “Closed geodesics on the surface of a simplex”, Sb. Math., 198:2 (2007), 243–260 | DOI | DOI | MR | Zbl

[4] A. A. Borisenko, D. D. Sukhorebska, “Simple closed geodesics on regular tetrahedra in Lobachevsky space”, Sb. Math., 211:5 (2020), 617–642 | DOI | DOI | MR | Zbl

[5] A. A. Borisenko, D. D. Sukhorebska, “Simple closed geodesics on regular tetrahedra in spherical space”, Sb. Math., 212:8 (2021), 1040–1067 | DOI | DOI | MR | Zbl

[6] A. A. Borisenko, “An estimation of the length of a convex curve in two-dimensional Aleksandrov spaces”, Zhurn. matem. fiz., anal., geom., 16:3 (2020), 221–227 | DOI | MR | Zbl