%0 Journal Article
%T Vertex-transitive maps on a torus
%A O. Such
%J ACTA MATHEMATICA 
UNIVERSITATIS COMENIANAE
%D 2011
%I Acta Mathematica Universitatis Comenianae
%X 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.
%K torus
%K wallpaper group
%K vertex-transitive map
%K Cayley map
%K semiregular tiling
%U http://www.iam.fmph.uniba.sk/amuc/_vol-80/_no_1/_such/such.pdf