Geodesic
Vertex-transitive maps on a torus
Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 1 
O. Such. Vertex-transitive maps on a torus. Acta mathematica Universitatis Comenianae, Tome 80 (2011) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2011_80_1_a0/
@article{AMUC_2011_80_1_a0,
     author = {O. Such},
     title = {Vertex-transitive maps on a torus},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2011},
     volume = {80},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2011_80_1_a0/}
}
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Voir la notice de l'article provenant de la source Comenius University

We examine FVT (free, vertex transitive) actions of wallpaper groups on semiregular tilings. By taking quotients by lattices we then obtain various families of FVT maps on a torus, and describe the presentations of groups acting on the torus. Altogether there are 29 families, 5 arising from the orientation preserving wallpaper groups and 2 from each of the remaining wallpaper groups. We prove that all vertex-transitive maps on torus admit an FVT map structure.