C60 Related Clusters
A hyper-structure is a (molecular) construction, of formula MY(mS; p) . n: M is the parent molecule in the Y “hyper”-building while m is the number of substructures S, joined by the type p facets; the total number n of atoms suffixes the name of the hyper-structure. Point-centered clusters and “cell-in-cell” clusters, used as seeds for map operations or even stellated “monomers” contributed to hyper-structure building, all based on the topology of M = C60(I h ). Examples are given starting from C750 = C60Y(60C20).750, transformed by dual, medial and truncation operations, to obtain hyper-structures of the type C60Y(60S;p).n.
Vertex equivalence classes found by topological descriptors were confirmed by permutations performed on the adjacency matrix associated to such complex graphs (by using Mathematica software). An atlas section illustrates the discussed multi-shell polyhedral clusters.
- Euler L (1752–1753) Elementa doctrinae solidorum-Demonstratio nonnullarum insignium proprietatum, quibus solida hedris planis inclusa sunt praedita. Novi Comment Acad Sc Imp Petropol 4:109–160Google Scholar
- Nagy CL (2016) Symmetry computation by Mathematica (to be published)Google Scholar
- Nagy CL, Diudea MV (2009) Nano studio software. Babes–Bolyai University, ClujGoogle Scholar
- Stefu M, Parvan-Moldovan A, Kooperazan-Moftakhar F, Diudea MV (2015) Topological symmetry of C60-related multi-shell clusters. MATCH Commun Math Comput Chem 74:273–284Google Scholar