Geodesic
Finite closed 5-loops of extended hyperbolic plane
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 38-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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There are four types of finite closed 5-loops which are invariant by the fundamental group $G$ and singled out on the extended hyperbolic plane $H^2$. It is proved that convex 5-loops belong to two types. The interior of the first type 5-loop coincides with the plane $H^2$. The 5-loop of the second type allows the partition into two simple loops of three and four dimension. Its interior coincides with the interior of the component of the simple 4-loop. The topological 5-loop properties are researched. 
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L. N. Romakina. Finite closed 5-loops of extended hyperbolic plane. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 11 (2011) no. 1, pp. 38-49. http://geodesic.mathdoc.fr/item/ISU_2011_11_1_a5/

[1] Romakina L. N., “Konechnye zamknutye 3(4)-kontury rasshirennoi giperbolicheskoi ploskosti”, Izv. Sarat. un-ta. Nov. ser. Matematika. Mekhanika. Informatika, 10:3 (2010), 14–26

[2] Romakina L. N., Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, Nauch. kniga, Saratov, 2008