All pentagonal face multi tori

TL;DR

This paper presents a method for designing all-pentagonal face multi-tori using map operations, analyzes their stability with computational chemistry, and describes their topology with Omega polynomial formulas.

Contribution

It introduces a novel design approach for multi-tori with all-pentagonal faces and provides topological and stability analyses of these structures.

Findings

Monomer and intermediates have moderate stability, between adamantane and C60.

Topological description using Omega polynomial is established.

Closed formulas for the Omega polynomial are derived.

Abstract

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.