Nonextremal coronoid

An extremal tuple coronoid shall frequently be identified by the symbol A in the following. A coronoid which is not extremal, is sometimes referred to as a nonextremal coronoid. 

In the second example of Par. 3.5.3 the unique smallest multiple coronoid for = 7 was derived from coronene according to the algorithm under consideration. Another such system emerges from C25H13 benzo[/u]anthanthrene. This nonextremal benzenoid has 25 internal vertices (iV) against = 24 (cf. Table 3). On the other hand, its minimum number of parallel... 

Here it is found by inspection that three naphthalene holes cannot be introduced in any of these benzenoids. Hence it is inferred that no triple coronoid with the formula C64H26 can be constructed. We must therefore look for the possibilities with h > h. Then the first case to be inspected is h = 18, corresponding to C68H28 and the associated benzenoids C68H22( =24, =30). These benzenoids are nonextremal and count 789 isomers (Stojmenovic et al. 1986 BrunvoU and Cyvin SJ 1990), a too large number to be inspected by sight, even if the depictions were available. However, two of these isomers perforated by three naphthalene holes, have actually been constructed (see Fig. 2) as the smallest catacondensed triple coronoids, in consistency with the present analysis. 

In other words, any extremal single coronoid (A) can be circumscribed without limitation. However, there also exist nonextremal single coronoids which are reproducible and therefore can be circumcscribed without limitation. Kekulene is an obvious example. 

Fig. 6.6. One isomer each of the smallest nonextremal extreme single coronoids. The inscribed numerals indicate the number of last added hexagon during the modified spiral walk.

Fig. 5.7. Examples of nonextremal extreme single coronoids which are not naphthalenic.

Formula. In accord with the above description every nonextremal extreme single coronoid (X) corresponds to an extremal single coronoid, A( ), for which A(hr-l) -i A(h) is accompanied by An = 2. The formulas of these special A coronoids are obtained from eqn. (57), but starting the running index from h = 1 i.e. h = 1, 2, 3, 4,...These A coronoids are associated with the... 

Property 6,4- A nonextremal extreme single coronoid X has never a fjord except for the inner fjords of its naphthalene hole if the system is naphthalenic. 

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