Full paper in PDF:
$% D. Singerman, Universal tessellations, Rev. Mat. Univ. Complut. Madrid 1 (1988), no. 1, 2, 3, 111–123.%$

Universal Tessellations

Department of Mathematics
University of Southampton
Southampton S09 5NH England

Received: January 22, 1988

All maps of type (m, n)  are covered by a universal map M(m, n)  which lies on one of the three simply connected Riemann surfaces; in fact M(m, n)  covers all maps of type (r,s)  where r| m  and s|n  . In this paper we construct a tessellation M  which is universal for all maps on all surfaces. We also consider the tessellation M(8,3)  which covers all triangular maps. This coincides with the well-known Farey tessellation and we find many connections between M(8,3)  and M  .

1980 Mathematics Subject Classification (1985 revision): 05C10, 20H05, 57M20, 10D07.