Holes and Polygons

It was said that kekulene (C of Fig. 1.1) and antikekulene (Fig. 1.7) exhibit an obvious resemblance, but this is a somewhat superficial viewpoint. The resemblance with kekulene is still more striking for another isomer of 43 2, viz. [12]drculene  

Both kekulene and [12]circulene,as well as antikekulene, can be interpreted as twelve polygons in a macrocycle. As such they are multiply connected polygonal systems with twelve polygons each. That is at least the current interpretation for kekulene. Antikekulene and [12]drculene on the other hand, are simply connected polygonal systems vdth thirteen hexagons each. 

When is a cycle the circumference of a polygon, and when does it surround a hole This is basically a matter of definition. A [ drculene, for instance, may either be interpreted as a simply connected polygonal system with q + I polygons as in the above discussion, but also as a multiply connected system with q hexagons. The latter interpretation has been adhered to several times even for C24H 2 [6]circulene, which is chemically indistinguishable from coronene (cf., e.g., Vol. 1—5.1 Cyvin BN, Brunvoll and Cyvin 1992b). 

The above convention excludes the interpretation of [ Jcirculenes as multiply connected systems. Notice that the above definition of a genuine perimeter implies, in the chemical context, that hydrogen atoms are attached to it. 

The above description explains much of the properties of the cluster system buckminsterfuUerene (Sect. 1.8). In the planar graph of Fig. 1.10 a pentagon was chosen as the boundary one could equally well choose a hexagon. 

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