Geodesic
Isometrics embedding in $E^3$ of some noncompact domains in the Lobachevskii plane
Sbornik. Mathematics, Tome 31 (1977) no. 1, pp. 1-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that all polygons in the Lobachevskii plane which have a finite number of vertices, as well as two wide classes of polygons with denumerably many vertices, can be regularly isometrically embedded in $E^3$. It is also shown that these polygons can be covered by a regular Chebyshev net. Bibliography: 4 titles. 
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È. G. Poznyak. Isometrics embedding in $E^3$ of some noncompact domains in the Lobachevskii plane. Sbornik. Mathematics, Tome 31 (1977) no. 1, pp. 1-27. http://geodesic.mathdoc.fr/item/SM_1977_31_1_a0/

[1] B. L. Rozhdestvenskii, “Sistema kvazilineinykh uravnenii teorii poverkhnostei”, DAN SSSR, 143:1 (1962), 50–52 | Zbl

[2] E. G. Poznyak, “O regulyarnoi realizatsii v tselom dvumernykh metrik otritsatelnoi krivizny”, DAN SSSR, 170:4 (1966), 786–789 | Zbl

[3] E. G. Poznyak, “O regulyarnoi realizatsii v tselom dvumernykh metrik otritsatelnoi krivizny”, Ukr. geom. sb., 1966, no. 3, 78–92 | Zbl

[4] V. F. Kagan, Osnovy teorii poverkhnostei, OGIZ, Moskva, 1948 | MR | Zbl