Various cages are constructed by using three types of caps: f-cap (derived from spherical fullerenes by deleting zones of various size), kf-cap (obtainable by cutting off the polar ring, of size k), and t-cap ("tubercule"-cap). Building ways are presented, some of them being possible isomerization routes in the real chemistry of fullerenes. Periodic cages with ((5,7)3) covering are modeled, and their constitutive typing enumeration is given. Spectral data revealed some electronic periodicity in fullerene clusters. Semiempirical and strain energy calculations complete their characterization.