EIGENVALUE SPECTRA OF LEAPFROG POLYHEDRA

Huckel magic-number rules for fullerenes, open nanotubes and polyhex t ori, though superficially different, are shown to have a common explan ation in eigenvalue theorems for the spectra of the trivalent polyhedr a produced by leapfrogging (omnicapping then dualising) trivalent poly hedral parents. A leapfrog polyhedron L, considered as a neutral all-c arbon pi system, will have a properly closed, meta-closed or open shel l, accordingly as the trivalent polyhedral parent P has at least one f ace of a size not divisible by three, or has at least one face of a si ze not divisible by six, or is an alternant with all face sizes divisi ble by six. Non-alternant L with all face sizes divisible by six are o f genus at least two and have meta-closed shells. Thus, leapfrog fulle renes have closed shells, leapfrog polyhex tori have open shells and l eapfrog infinite nanotubes are metallic in the Huckel model.