engleski

Computer enumeration of space fullerenes

A fullerene is a 3-valent plane graphs whose faces are pentagons and hexagons. A fullerene is said to be IHR if its hexagons are adjacent, i.e. are adjacent only to pentagons. A space fullerene is a 4-valent tiling of the space by IHR fullerenes. Space fullerenes are interesting in crystallography and in Discrete geometry. There are exactly 4 IHR fullerenes of symmetry Ih, D6d, Td and D3h. We enumerates the space fullerenes with a small fundamental domain under their translation groups. The technique is decomposed into two steps: The use of Delaney symbols, i.e. flag systems, as the basic model for storing combinatorial informations and the use of the softwares 3dt and Systre by Olaf Delgado for transforming combinatorial description into topological and metric ones. The design of programs for enumerating space fullerenes, using all the tricks in the books of combinatorial enumeration in order to achive the highest speed possible.

Delaney symbol; crystallography; enumeration; fullerene

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