Mathematics Ph.D. Dissertations


The Classification of l1-embeddable Fullerenes

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)


Mathematics/Mathematics (Pure)

First Advisor

Sergey Shpectorov (Advisor)


In Chemistry, fullerenes are molecules composed entirely of carbon atoms, in the form of a hollow sphere, ellipsoid or tube, such that each atom is bonded with three other atoms and the atoms form pentagonal or hexagonal rings. The spherical fullerenes motivated the related mathematical concept: a fullerene graph is a trivalent plane graph such that all faces are pentagons and hexagons. The goal of this research is to prove the conjecture that there are exactly five l1-embeddable fullerenes. These are known to be the following fullerenes: F20(Ih),F26(D3h), F40(Td), F44(T), F80(Ih) (where the group of symmetry is given in parentheses for each fullerene). We proceed in proving this result by looking at the minimal distance between the pentagonal faces of the fullerene. In the cases when the minimal distance between pentagons is greater than two we obtain a contradiction, which leads us to conclude that in an l1-embeddable fullerene there must exist at least two pentagons that either are adjacent or have a common hexagonal neighbor. For the latter cases we show that the only possibilities are the five fullerenes listed above.