The Structure of Fullerene Signatures
نویسنده
چکیده
This paper is devoted to developing the structure of fullerene signatures. These structure results are then used to construct a complete catalog of fullerenes with ten or more symmetries. These fullerenes fall into 112 families. The Coxeter fullerenes, obtained by subdividing the faces of the icosahedron, form the prototype family. Like the Coxeter families, each family in the catalog is a one, two, three or four parameter collection of labelings of a fixed planar graph on 12 vertices. The actual fullerenes are obtained by assigning positive integers to the parameters and filling in the faces of the plane graph with the regions from the hexagonal tessellation of the plane determined by the parameter values.
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