Minimal-volume conjecture for fullerenes with 6k-4 atoms

Let $C_N$ be the class of fullerene isomers with $N$ atoms. Suppose $N=6k-4\neq 10s$, where $k\geq 5$ and $s\geq 2$. A nanotubical fullerene has a tubular part and two caps, and caps of types (a) and (b) are the cap types considered here. Minimal-volume conjecture for fullerenes with 6k-4 atoms. If a fullerene with $N=6k-4\neq 10s$ atoms, $k\geq 5$, $s\geq 2$, has the minimal hyperbolic volume in the class $C_N$, then it is a nanotubical fullerene with caps of type (b). If fullerenes with caps of types (a) and (b) have the same number of atoms, $N=10k$, then the fullerene with caps of type (a) has the minimal hyperbolic volume. The assertion extends the proposed pattern relating cap types, Wiener index, and hyperbolic volume beyond the $N=10k$ case; no proof is supplied for arbitrary $N$.