Isohedral tilings on Riemann surfaces of genus~2
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 17-28.

Voir la notice de l'article provenant de la source Math-Net.Ru

3 Riemann surfaces which possess rich metrics are considered. In previous paper [1] the classification of fundamental isohedral tilings for groups of conformal automorphisms of these surfaces was obtained. Here the classification of fundamental isohedral tilings is obtained for groups of conformal and anticonformal automorphisms of the surfaces. The tilings are given by the adjacency symbols of the corresponding tilings on the universal covering hyperbolic plane.
@article{BASM_2012_2_a1,
     author = {Elizaveta Zamorzaeva},
     title = {Isohedral tilings on {Riemann} surfaces of genus~2},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {17--28},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a1/}
}
TY  - JOUR
AU  - Elizaveta Zamorzaeva
TI  - Isohedral tilings on Riemann surfaces of genus~2
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2012
SP  - 17
EP  - 28
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a1/
LA  - en
ID  - BASM_2012_2_a1
ER  - 
%0 Journal Article
%A Elizaveta Zamorzaeva
%T Isohedral tilings on Riemann surfaces of genus~2
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2012
%P 17-28
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a1/
%G en
%F BASM_2012_2_a1
Elizaveta Zamorzaeva. Isohedral tilings on Riemann surfaces of genus~2. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2012), pp. 17-28. https://geodesic-test.mathdoc.fr/item/BASM_2012_2_a1/

[1] Zamorzaeva E. A., “On the classification of tilings on Riemann surfaces of genus two”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2000, no. 2, 39–50 | MR | Zbl

[2] Bilinski S., “Homogene Netze geschlossener orientierbarer Flächen”, Bull. Internat. Acad. Yougoslave, Cl. Sci. Math. Phys. Tech. (N.S.), 6 (1952), 59–75 | MR

[3] Franz R., Huson D. H., “The classification of quasi-regular polyhedra of genus 2”, Discrete Comput. Geom., 7 (1992), 347–357 | DOI | MR | Zbl

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

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

[6] 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

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

[8] Molnár E., Stettner E., “Symmetry groups and fundamental tilings for the compact surface of genus 3. II. The normalizer diagram with classification”, Beiträge Algebra Geometrie, 46 (2005), 19–42 | MR | Zbl

[9] Bujalance E., Singerman D., “The symmetry type of a Riemann surface”, Proc. London Math. Soc. (3), 51 (1981), 501–519 | DOI | MR

[10] 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

[11] Zamorzaeva E., “Classification of isohedral tilings of the Riemann surface with the automorphism group $G_{24}^\ast$”, International Seminar on Discrete Geometry dedicated to the 75th birthday of Professor A. M. Zamorzaev, Communications, Chisinau, 2002, 113–118 (in Russian) | MR

[12] Conway J. H., “The orbifold notation for surface groups”, Combinatirics and Geometry, London Math. Soc. Lecture Notes Series, 164, Cambridge University Press, Cambridge, 1992, 438–447 | MR

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

[14] Delone B. N., “Theory of planigons”, Izvestiya Akad. Nauk SSSR. Ser. Matem., 23:3 (1959), 365–386 (in Russian) | MR | Zbl

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