A catalogue of isomerization transformations of fullerene polyhedra

Representation of isomerization and carbon insertion or extrusion mechanisms as patch replacements on a fullerene surface allows construction of a catalogue of topologically distinct local transformations of fullerenes, classified by patch boundary and pentagon content. All isomerization patches and isomerization pairs containing up to five pentagons and with an upper limit for the boundary length depending on the number of pentagons are listed. Several infinite series of transformations are identified.