All pentagonal face multi tori

Design of monomeric unit, by using sequences of map operations, and the growing process in the building of a double-shell multi torus with all-pentagonal faces, is presented. It is shown that the monomer and some small intermediates, as hydrogenated species, have a moderate stability, between adamantane and C60 fullerene, as calculated at the PM3 level of theory. The topology of these high genera structures is described in terms of Omega polynomial as a function of the net parameters. Closed formulas for this polynomial and examples are presented.