A theoretical and computational study of the lowest lying triplet state df cyclic hydrocarbons having an even number (2n) of pi electron bonds (antiaromatic compounds) is presented. In these systems, the ground singlet state of the most symmetric structure is distortive, being a transition state for the reaction exchanging two bond-alternating structures. As a resonance hybrid of two equivalent valence bond (VB) structures, this singlet is a stabilized biradical of B-1g symmetry. The lowest lying triplet of the most symmetric form is strongly bound, similar in geometry to the 1(1)B(1g) singlet transition state, and is always higher in energy. The energy difference between the two states is remarkably constant regardless of the ring size. This apparent violation of Hund's rule is derived from the symmetry properties of the system. The triplet state is treated as a resonance hybrid of n equivalent covalent structures, each having n - 1 singlet electron pairs and one pair of two spin parallel electrons (triplet pair); part of the exchange resonance stabilization is lost in the triplet, making the singlet more stable. Thus, this effect is due to the difference between the static resonance stabilization of the triplet and the singlet states. In contrast, Hund's rule always holds for biradical systems having only one dominant VB structure. Spectroscopic observation of these biradical triplets is possible by photodetaching an electron from the monoanion, as recently demonstrated experimentally. The model predictions are confirmed computationally for several examples including H-4, H-8, cyclobutadiene, cyclooctatetraene, pentalene, and heptalene.