Nonextremal Extreme Single Coronoids

Notation and Preliminary Treatment. Let an extreme single coronoid which is not extremal be identified by X(n 5 ). These formulas occur for certain values of n- = n, but not 

Instead of this elaborate specification of the (n s ) formulas we are able to derive explicit expressions for the coefficients of these formulas. Before this derivation some additional properties of the X coronoids are to be treated as a preparation. 

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 

The final expressions are readily obtained from eqn. (57), where the parameter h should have the 

Here an alternative derivation of eqn. (81) is again possible because of the known expressions (Cyvin SJ 1992c) 

---

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.

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. 

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. 

---