Abstract: MATH/CHEM/COMP 2002, Dubrovnik, June 24-29, 2002

Gothic Fullerenes

Tomaz Pisanski

IMFM, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia

Ceilings of Gothic churches containing ribbed vaults present interesting mathematical patterns. A ribbed vault is a framework of diagonal arched ribs carrying the cells which cover ceiling in the spaces between them. Such a structure can be represented as a graph on a surface. The bosses and columns are vertices, the ribbed arches are edges and the cells are faces of the embedded graph. Such geometric patterns can be found in Gothic churches throughout Europe. In some cases the complicated structure of such patterns can be explained by applying some transformations which turn the simple, smaller graphs into larger, more complicated ones. By combining simple transformations into more complicated ones a powerful tool for investigating maps on surfaces and polyhedra is obtained. For instance, in the study of fullerenes the most useful transformations map fullerenes to fullerenes. Two of such transformations have been studied intensively, the leapfrog and the chamfering operations. From mathematical viewpoint it also make sense to apply the gothic transformation to fullerene. It is on chemists to tell whether the result has a chemical interpretation.