Type 1 conjecture for fullerene nanodiscs

A fullerene nanodisc $D_r$ is a fullerene nanodisc indexed by an integer $r$. Type 1 conjecture. The fullerene nanodiscs $D_r$, for every integer $r\geq 2$, are Type 1. The conjecture would classify the entire family of fullerene nanodiscs with indices at least $2$ as Type 1, extending the paper's result for $r=5+3k$ with $k\in\mathbb{Z}^{+}$ and supporting Brinkmann, Preissmann and Sasaki's conjecture.