Forma, Vol. 19 (No. 3), pp. 131-163, 2004
Original Paper

Covering Forms in Nanostructures

Mircea V. Diudea

Faculty of Chemistry and Chemical Engineering, Babes-Bolyai University, 400028 Cluj, Romania
E-mail address:

(Received September 28, 2004; Accepted March 8, 2005)

Keywords: Operations on Maps, Stone-Wales Edge Flipping, Corannulenic Systems, Nanostructures

Abstract. Various covering lattices, encountered in spherical and tubular nanostructures, can be achieved, mainly by: (i) operations on maps; (ii) cutting procedures and (iii) Stone-Wales SW edge rotations. The most versatile and deeply involved in the electronic structure of nano-molecules are some geometrical-topological operations on maps, including the newly proposed septupling operations.
A disjoint corannulenic system DCorS is proposed, by analogy to the well-known perfect Clar system PCS, in connection to some supra-organized fully-resonant -electronic aromatic systems of nanostructures. The constructive demands for such DCorS are given.
Cutting procedures have been developed for the generation of large sized tubular and toroidal objects, of various covering, associated to nanostructures. Stone-Wales edge rotations enabled covering changes in both spherical and tubular objects. Several new coverings and routes of possible isomerization reactions were identified by this procedure.
Supramolecular graphitoids, as infinite periodic surfaces of negative curvature and genus higher than zero, is shown to be constructible by self-assembly of various repeat units, some of them appearing as 3D junctions of nanotubes. In this respect, new representations of the Dyck graph are proposed.

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