The Face Consistency and Embeddability of Fullerenes: Orange Peel Fullerenes

A fullerene is a carbon molecule where each carbon atom is chemically bonded to three other carbon atoms and the atoms form pentagonal and hexagonal rings and this molecule can be viewed as a finite connected trivalent plane graph, all of whose faces are pentagons and hexagons. Some research has focused on the graph theoretical properties of fullerenes and in some cases trying to determine a relationship between a graph theoretical property and chemical properties of the molecule. In this research we will focus on the graph theoretical property of a graph being l_1-embeddable and discuss the face consistency of a particular class of fullerenes. This class is the hexagonal orange peel fullerenes with the symmetry group D_{6h} and the pentagonal orange peel fullerenes with the symmetry groups D_{5h} or I.