These plane soccer tori give us a number of symmetric tilings of the plane by regular polygons. Indeed here is a table of the number of triangular tilings as a function of the genus. As in the case of a torus, there is no conformal model in three dimensional space that perfectly captures the angle an length relations for the tiling or the soccer pattern. Moreover one cannot represent the symmetries of the soccer pattern by rotations and reflections of the surface as we can with the sphere. The construction of the identification of sides and the soccer patterns is left to the interested reader.
Soccer ball patterns on the sphere .
This page last updated on 21 Apr 01.