Minimal-volume conjecture for exceptional-order fullerenes

Let $C_N$ be the class of fullerene isomers with $N$ atoms. Assume $N\neq 20,24,26,28,34$, $N\neq 10s$, and $N\neq 6k-4$, where $k\geq 5$ and $s\geq 2$. A nanotubical fullerene graph has a tubular part and two caps, with caps of types (c) and (d) among the possible cap types. Minimal-volume conjecture for exceptional-order fullerenes. If a fullerene isomer with number of atoms $N$ has the minimal hyperbolic volume in the class $C_N$, then it is a nanotubical fullerene graph with caps of type (c) or (d). Computations cited in the paper identify the relevant cap classes for all $N\leq 216$ subject to the stated exclusions, but the conjecture asserts the structural conclusion in general.