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Conventional organic chemistry shows that a molecule must also be cyclic and planar to be aromatic. While cyclobutadiene is planar, cyclooctatetraene exists as a tub. A topological analysis of this molecule reveals the presence of two rings, made up of the same constituent atoms, bounding a cage critical point. The existence of a cage critical point bounded by only two rings has been discussed as a mathematical possibility by Bader. However until now the minimum number of rings observed has been three, e.g. bicyclo[1.1.1]pentane.
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