A Catalogue of Isomerization Transformations of Fullerene Polyhedra

Abstract

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.

Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes

“…NS fullerenes can conveniently be constructed through vertex insertions or from smaller fullerenes, which contain a face spiral. A list of possible vertex transformations and insertions has been given by Brinkmann and Fowler Here, we use four Yoshida‐Fowler four‐vertex insertions to transform T ‐C 364 → T ‐C 380 , and three Brinkmann–Fowler six‐vertex insertions to transform D 3 ‐C 366 → D 3 ‐C 384 , that is, see Figure . The two NS fullerenes C 380 and C 384 are shown in Figure , and the two corresponding smaller fullerenes used for the construction, C 364 and C 366 , are depicted in Figure .…”

“…Brinkmann and Fowler presented a catalog of possible isomerization transformations and vertex insertions as patch replacements in fullerenes . Currently implemented in this program are Stone–Wales transformations, Endo–Kroto two‐vertex insertion, Yoshida–Fowler four‐ and six‐vertex insertions, and Brinkmann–Fowler six‐vertex insertion .…”

“…NS fullerenes can conveniently be constructed through vertex insertions or from smaller fullerenes, which contain a face spiral. A list of possible vertex transformations and insertions has been given by Brinkmann and Fowler [54,55] Here, we use four Yoshida-Fowler four-vertex insertions to transform T-C 364…”

The topology of fullerenes

“…Astakhova et al 88 extended this rearrangement mechanism even further to higher numbers of pentagons. Brinkmann et al 83 generated a catalog of isomerization pairs with up to five pentagons.…”

A Catalogue of Growth Transformations of Fullerene Polyhedra

“…Previous work has established the utility of the notion of patch replacement as a common framework for representation and classification of isomerization and growth/carbon-loss transformations. A systematic catalogue of isomerization transformations based on this approach has been constructed …”