An overview of magnetic circular dichroism (MCD) spectroscopy of π‐electron systems derived from a 4N‐electron perimeter is provided, with emphasis on the hypothetical parent cycloocta‐1,3,5,7‐tetraene of D8h symmetry (1) and its D4h symmetry derivatives. UV‐visible absorption and MCD spectra of 2, a D4h symmetric cycloocta‐1,3,5,7‐tetraene planarized by the effect of 4 bicyclo[2.1.1]hexeno units fused to its 8‐membered ring, are reported and interpreted. The perimeter model is applied to obtain an understanding of the nature of electronic states in 1 and 2 and to predict general trends in the spectra. The electronic excitation patterns are found to be different in the antiaromatic D8h and unaromatic D4h species, and their states cannot be unequivocally correlated. The results of time‐dependent density functional theory and extended multistate complete active space second‐order perturbation theory (XMS‐CASPT2) computations agree with the algebraic perimeter model analysis and reproduce the spectra of 2 well, including three of the four observed MCD signs of A and B terms.