Most of the literature concerning the definition of organic reefs (bioherms and biostromes) and of similar carbonate accumulations emphasizes the genetic and biostratigraphic classification of these features. To the writer's knowledge, no previous attempt has been made at a purely morphological classification. "Reef complexes" have in recent years been called "bank atolls," "reef-fringed carbonate banks," and "biohermal flanked biostromes." Such hybrid names appear to impose a dualistic origin on a reef complex, although it is obviously a genetic unit, and they should therefore be avoided. Henson's "reef complex" included the sediments genetically associated with the reef sensu stricto; these are not "banks" or "biostromes" within the generally accepted meaning of these t rms. The writer therefore has introduced the term "cycloherms" (circular reefs) for the gigantic shelf atolls such as those in the Devonian of western Canada, in the Permo-Pennsylvanian of West Texas, and in the Cretaceous of Mexico. In addition, the term "phragmoherms" (wall reefs) was introduced for fringing reefs and barrier reefs such as those in the Triassic of the Alps.

In recent years bioherms proper have been called "pinnacle reefs," "haystack reefs," and other such terms which bear little relation to their actual morphologic proportions. Such names are based on the reef shapes commonly seen in cross sections of exaggerated vertical scale, and create erroneous impressions of their true relative dimensions. The new, unequivocal names proposed for these bioherms are "aspiherms" (shield reefs) for the pinnacle type and "trapeziherms" (table reefs) for the flat-topped haystack type.

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