Abstract: MATH/CHEM/COMP 2002, Dubrovnik,
June 2429, 2002

Gothic Fullerenes
Tomaz Pisanski IMFM, University of Ljubljana, Jadranska 19, SI1000 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. 