This talk will complement the first talk of the term on Cayley maps given by Robert Jajcay. The underlying link between the two talks will be the beautiful patterns on surfaces and computational power of group theory as a classifying tool. The underlying mathematical question is to classify all finite groups of transformations of closed surfaces. However, the approach to classification presented will be strongly linked to the underlying geometry and maps of the surfaces. The first part of the talk will link the groups of transformations of the sphere and torus to soccer balls, the platonic solids, and tessellations of the plane. The second part of the talk will venture into genus 2 surfaces and beyond.

There will be plenty of pictures – see for instance http://www.rose-hulman.edu/~brought/Epubs/soccer/soccerpics.html