Asymptotic prevalence of asymmetric IPR fullerenes

Establish whether the proportion of asymmetric IPR fullerenes tends to 1 as the number of vertices increases.

Background

The paper reports that the proportion of asymmetric IPR fullerenes exceeds 94% at 118 vertices and trends upward over the computed range, although not monotonically. It raises the unresolved issue of whether this proportion converges to 1 for larger fullerene sizes.

References

Over the computed range the proportion of asymmetric IPR fullerenes trends upward, though not monotonically---it dips at $n = 88, 96, 104, 108, 112$ and $116$---and exceeds $94\%$ at $n = 118$; this is consistent with a tendency toward $1$, for which we are not aware of a proof.

— Extremal Asymmetric Depth of Planar Graphs and Hidden Near-Mirror Symmetries of IPR Fullerenes  (2609.02585 - Pastorek, 2 Sep 2026) in Section 1, Motivation and Background