How Many Rings Can Share a Quaternary Atom?

With only primary branching, six rings may share a quaternary vertex; with secondary branching, 12 rings may be accommodated. There are two primary bicyclic systems (spiro and fused) and an additional (bridged) system when branching is considered. There are three primary tricyclic systems, termed monofuso, difuso, and trifuso (depending on the number of fusion bonds present); there are another six tricyclic systems involving secondary branching; and examples of all nine tricyclic classes are known. Without secondary branching there are two tetracyclic (trifuso and tetrafuso) and one each pentacyclic and hexacyclic classes. While the tetracyclic and higher classes with secondary branching have not been enumerated, T_d tetraadamantane is shown to possess 12 rings, the maximum possible for this class. Centropolycyclics with three-, four-, five-, and six-membered rings are enumerated and their strain energies are calculated. Although many of these polycyclic systems are known, some unknown ones are energetically accessible and should be stable. For the five-membered ring derivatives (polyquinanes), it is suggested that a small family of polydodecahedranes, analogous to the adamantanes, would be stable. When different ring sizes are allowed, a large number of polycyclics are possible. Strain calculations suggest that the five kinds of unbridged tricyclics containing three-, four-, and five-membered rings should all be reasonably stable. The proposed scheme may find use in categorizing the voluminous literature of polycyclic natural products, including alkaloids. Thus, despite a literature statement that difusotricyclics “remain rare”, cephalotaxine, phytotuberin, and the cytochalasins fit this category.