Polygonal system

A mono- polyhex (Cyvin 1992a) is a polygonal system with exactly one q-gon and otherwise hexagons (if any). For 9=6 these systems reduce to polyhexes. The fluoranthenoids (hydrocarbons) contain fluoranthene as a key molecule and have in general even-carbon 

The mono— hexagonal lattices (Cyvin 1992a) are analogous with the hexagonal lattice. Examples for = 5 and = 7 are shown below. 

In both cases of the above diagram, the perimeter of [ drculene viz. [5]circulene and [7]circulene, are drawn by heavy Unes (cf. Vol. 1—1.3, and notice in particular that corannulene is identical with [5]circulene). 

The introduction of mono- hexagonal lattices makes it feasible to adapt the notions of geometrically planar/nonplanar and nonhelicenic/helicenic systems to mono—(f-polyhexes in general. 

---

Isomer Enumeration of Unbranched Catacondensed Polygonal Systems with Pentagons and Heptagons. 

The polygonal system of the annulenes can be extended to polyhedral systems of equivalent atoms. Atoms are equivalent if the symmetry group of the molecule—or... 

CLASSIFICATIONS OF POLYGONAL SYSTEMS, AND SOME ASPECTS OF KEKULE STRUCTURES... 

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). 

Symmetry Considerations. Symmetry has been exploited systematically many times in different enumeration problems. The references cited in Brunvoll, Cyvin BN and Cyvin (1993c), even when confined to enumerations of polygonal systems (Balaban and Harary 1968 Harary and Read 1970 Balaban 1970 Lunnon 1972), are far from exhaustive. A coronoid (or in general a polyhex) may belong to one of eight symmetry groups cf. Vol. I-3.3.8 and Table 5. Here all... 

By passing we wish to point out a feature, which often is encountered in different kinds of enumeration the total numbers are the same as those of the unsymmetrical systems, but shifted one place on the list cf., e.g., the results on some polygonal systems representing polycydic conjugated hydrocarbons with arbitrary ring sizes (BrunvoU, Cyvin BN and Cyvin 1993a). The below diagram and table are supposed to elucidate the feature in question. 

Morikawa T, Balaban AT (1992) Topological Formulas and Upper/Lower Bounds in Chemical Polygonal Systems, Particularly in Benzenoid Polyhexes. Match 28 235... 

---