ABSTRACT
The idea of the dualist graph based on the bidimensional graphite lattice can be extended to the tridimensional diamond lattice. In this case, catamantanes (e.g. adamantane, the diamantanes, etc.) have dualist graphs which are isomorphic to the staggered rotamers of alkanes. Such rotamer graphs may be coded by four digits (1,2,3,4) according to the four directions of the C-C bonds in the diamond lattice, and then adopting the convention of minimal resulting number [126-128]. Thus, staggered n-butane (which is the dualist graph of tetracatamantanes) can have either the transoid conformation, 54 (coded by 121), or one of the two enantiomeric gauche conformations, 55 (123) or 56 (124). Formulas were devised for enumerating all the possible staggered conformera of linear or branched alkanes, and of cycloalkanes [126].
