Periodoannulene molecules and ions C x I x q in planar geometry offer examples of systems with the potential for outer σ and inner π ring-current double aromaticity, given a sufficient overlap of tangential p σ -orbital manifolds on the large atoms of the outer cycle. Previous theoretical work indicated concentric diatropic currents in the dication C 6 I 6 2+ . Ab initio ipsocentric calculations support an account in terms of frontier-orbital selection rules for current contributions in C 6 I 6 2+ (and radical C 6 I 6 +, implicated in recent experimental work on the oxidation of periodobenzene). A σ/π analogue of the annulene-within-anannulene model is applied here to periodo systems based on cyclooctatetraene. Model species C 8 I 8 q with charges q = 0, +1, +2, +4, −2 and structures constrained to a planar D 4h symmetry exhibit maps with all combinations of σ/π con-and counter-rotation, comprising global σ ring currents on the iodine perimeter and central π ring currents on the carbocycle. All can be rationalized by the separate application of the tropicity selection rules to the two subsystems, whether in singlet or triplet states.