Literature Cited
H. C. Wilkie, “On non-Euclidean crystallographic groups,” Math. Z.,91, No. 2, 87–102 (1966).
R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Funktionen, Leipzig, Vol. 1, (1926), pp. 285–315.
L. Keen, “Canonical polygons for finitely generated fuchsian groups,” Acta Math.,115, Nos. 1–2, 1–16 (1966).
A. M. Macbeath, “The classification of non-Euclidean plane crystallographic groups,” Can. J. Math.,19, No. 6, 1192–1206 (1967).
L. Bers, “Uniformization by Beltrami equations,” Commun. Pure Appl. Math.,14, 215–228 (1961).
N. L. Alling and N. Greenleaf, Foundations on the Theory of Klein Surfaces, Springer-Verlag, Berlin-Heidelberg-New York (1971).
B. Maskit, “On Poincare's theorem for fundamental polygons,” Adv. Math.,7, No. 2, 219–230 (1971).
A. F. Beardon, “Hyperbolic polygons and Fuchsian groups,” J. London Math. Soc.,20, No. 2, 247–255 (1979).
J. Lehner, Discontinuous Groups and Automorphic Functions, Am. Math. Soc., Providence, RI (1964).
P. Tukia, “On discrete groups of the unit disk and their isomorphisms” Ann. Acad. Sci. Fenn. Ser. A I,504, 1–45 (1972).
S. M. Natanzon, “Invariant lines of Fuchsian groups,” Usp. Mat. Nauk,27, No. 4, 145–160 (1972).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 26, No. 4, pp. 137–143, July–August, 1985.
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Potyagailo, L.D. Fundamental polygonal groups of non-Euclidean crystallography. Sib Math J 26, 586–591 (1985). https://doi.org/10.1007/BF00971306
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DOI: https://doi.org/10.1007/BF00971306