Ring-current aromaticity of icosahedral C-120 archimedene is probed at the ipsocentric/6-31G* level by direct mapping of the current density induced in its 4-, 6- and 10-sided faces by perpendicular magnetic fields. In contrast to planar phenylene analogues, the 4-faces (and only those faces) support global pi ring currents: intense., paratropic (antiaromatic), stronger on the cage interior. The results validate a simple pseudo-pi hydrogen-cluster model for curved carbon networks. Its application to - and fullerenes shows dominant paratropic ring currents in pentagons militating against attribution of global aromaticity. Application to octahedral derivatives C60X12, shows eight 'aromatised' hexagonal rings.