Perfect and Imperfect Extremal Coronoids

From the definition of extremal polyhexes (Par. 3.3.4) it is clear that there exists an extremal polyhex for every possible value of h when g is fixed. Let it be symbolized 

Some introductory observations about extremal coronoids are reported below. They are foUowed by comments which tend to justify the inherent assumptions. However, the observations are not to be considered as rigorously proved. 

If A (/i) is a perfect extremal coronoid, then all the larger extremal coronoids A h ) for h h are also perfect. 

In connection with Observation 1, suppose that a coronoid C has a corona hole larger than naphthalene. Then we can imagine that a closer packing of the hexagons of C is possible by a partial filling of the corona hole so that the total number of internal vertices increases. In Observation 2 the crucial term ( perfect extremal coronoid ) conforms with Definition 3.5 of Par. 3.3.4. It is reasonable to imagine that there is a critical smallest size for an extremal benzenoid, say A, so that A can be perforated with g naphthalene holes, which is taken to be the necessary condition for creating a perfect extremal tuple coronoid. 

Consider two extremal coronoids AJ h) and A (/i), along with their associated benzenoids, say B and B, respectively. Here B may be identical with B, namely if it is possible to perforate B = B by naphthalene holes in two different ways so as to create the two nonisomorphic systems A (h) and A h), In general B and B must have the same invariants as indicated by B(H,iNT), B (H,A ). This is a consequence of Observation 1. It foUows that B and B also have the same formula, say C yH, and the same perimeter length, say N. The connections 

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