Isohedral tilings for hyperbolic translation group of genus two which admit additional isometries
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 30-43.

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The paper continues articles [3, 4] where we derived all the Delone classes of isohedral tilings of the hyperbolic plane with disks for the translation group of genus two. The total number of these Delone classes is corrected to 118. The attention is drawn to the parametric diversity of these tilings. The emphasis is made on more symmetric tilings that are promising for further research and application. Isohedral tilings that admit additional isometries are analyzed, their adjacency diagrams are shown in figures.
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Elizaveta Zamorzaeva. Isohedral tilings for hyperbolic translation group of genus two which admit additional isometries. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2020), pp. 30-43. https://geodesic-test.mathdoc.fr/item/BASM_2020_2_a3/

[1] Macbeath A. M., “The classification of non-Euclidean plane crystallographic groups”, Canad. J. Math., 19 (1967), 1192–1205 | DOI | MR | Zbl

[2] Conway J. H., “The orbifold notation for surface groups”, Groups, Combinatorics and Geometry, London Math. Soc. Lecture Note Series, 165, Cambridge University Press, 1992, 438–447 | MR | Zbl

[3] Zamorzaeva E., “Isohedral tilings by 8-, 10- and 12-gons for hyperbolic translation group of genus two”, Bul. Acad. Ştiinţe Repub. Moldova. Mat., 2018, no. 2, 74–84 | MR | Zbl

[4] Zamorzaeva E., “Isohedral tilings by 14-, 16- and 18-gons for hyperbolic translation group of genus two”, Bul. Acad. Ştiinţe Repub. Moldova. Mat., 2019, no. 1, 91–102 | MR | Zbl

[5] Coxeter H. S. M., Moser W. O. J., Generators and Relations for Discrete Groups, 4th ed., Springer, Berlin–Heidelberg–New York, 1980 | MR | Zbl

[6] Delone B. N., “Theory of planigons”, Izvestiya Akad. Nauk SSSR. Ser. Matem., 23 (1959), 365–386 (in Russian) | MR | Zbl

[7] Proc. Steklov Inst. Math., 4 (1980), 111–141 | MR | Zbl

[8] Grünbaum B., Shephard G. C., Tilings and Patterns, Freeman, New York, 1987 | MR | Zbl

[9] Lučić Z., Molnár E., “Combinatorial classification of fundamental domains of finite area for planar discontinuous isometry groups”, Archiv der Matematik, 54 (1990), 511–520 | MR

[10] Lučić Z., Molnár E., “Fundamental domains for planar discontinuous groups and uniform tilings”, Geom. Dedicata, 40 (1991), 125–143 | DOI | MR

[11] Huson D. H., “The generation and classification of tile-$k$-transitive tilings of the Euclidean plane, the sphere and the hyperbolic plane”, Geom. Dedicata, 47 (1993), 269–296 | DOI | MR | Zbl

[12] Balke L., Huson D. H., “Two-dimensional groups, orbifolds and tilings”, Geom. Dedicata, 60 (1996), 89–106 | DOI | MR | Zbl

[13] Zamorzaeva E., “On isohedral tilings of hyperbolic manifolds”, Analele Ştiinţifice ale Universităţii 'Al. I. Cuza' Iaşi, s. 1a, Matematică, 59:1 (1997), 81–88 | MR

[14] Zieschang H., Vogt E., Coldewey H. D., Surfaces and Planar Discontinues Groups, Lecture Notes in Mathematics, 835, Springer-Verlag, New York, 1980 | DOI | MR