The Huckel-London-Pople-McWeeny (topological) approach for calculating pi-electron ring currents and bond currents in conjugated systems is applied to the structures altan-corannulene and altan-coronene, recently designed by Monaco and Zanasi. These authors applied the ab initio ipso-centric formalism to calculate pi-electron current-density maps and individual bond current intensities in these structures. In a parallel investigation the key findings of Monaco and Zanasi's ab initio study are here qualitatively confirmed by this much more rudimentary topological assessment: namely, that, in their three layers, the two structures altan-corannulene and altan-coronene reveal patterns of contra-rotating paramagnetic/diamagnetic/paramagnetic pi-electron circulations in their innermost, middle, and outer cycles, respectively.