The ring-current aromaticity of the bicalicene molecule arises, in spite of the 16 π carbon perimeter, from strong local diatropic circulations on the two pentagonal rings, as shown by current-density maps computed at the ipsocentric RHF/6-311G** and DFT/6-311G** levels of theory. Conjugated-circuit models cannot capture this pattern of circulation as it arises from 'ionic' contributions in a valence-bond picture. Canonical molecular-orbital analysis reveals a cancellation of paratropic and diatropic frontier-orbital contributions, which explains the difficulties that Hückel-based models have in producing qualitatively correct current-density maps for this molecule. Other measures of aromaticity reflect, to different extents, the dominance of the 'tetraionic' contribution to the aromaticity of this species.