SPHEROALCANES MODELS AS EXAMPLES OF SHAPE S CORRESPONDING TO DIFFERENT SYMMETRY POINT-GROUPS

This paper presents systematic construction of the planar formula of t he smallest spheroalcanes (i.e. (CH)(N) molecules, N even, of which th e planar formula is a simple, trivalent, planar graph) whose topologic al symmetry (i.e. their conformation of highest symmetry whatever thei r stable conformation) belongs to any finite point-group. Two-dimensio nal point-groups are first considered; it is shown that appropriate co mbination of greek letters Gamma and Delta may give example of those g roups. We propose to use the symbols Gamma(n) and Delta(n), similar,to Bose of the Schonflies system for 3-D point-groups, for the 2-D point -groups called respectively n and nm (n even) or nmm (n odd) in the He rmann-Mauguin system. It is shown that objets belonging to any finite axial point-group may be obtained by placing a number of Gamma or Delt a on the surface of a cylinder of revolution in suitable positions. Si milarly, the formula for spheroalcanes of the corresponding symmetry m ay generally be obtained by a cylinder-like combination of(CH)(2q) fra gments (1 less than or equal to q less than or equal to 6), of valency v = 2, 4 or 6 of the appropriate shape. A list of such fragments is g iven. The formula of spheroalcanes with (topological) high-symmetry ma y-be obtained from the graphs of selected regular and semi-regular pol yhedra. A brief review of spheroalcanes already known experimentally a nd/or studied theoretically is given at the end of this paper.