Patch replacements recovering global mirror symmetry

Construct fullerene patch replacement operations that recover the underlying global mirror symmetries associated with the near-mirror partial automorphisms observed in asymmetric IPR fullerenes of depth $2$ and $3.

Background

The low-depth IPR fullerenes studied in the paper exhibit partial symmetries that appear to be broken versions of global mirror symmetries. The author reports unsuccessful attempts to recover those global symmetries using known simple patch replacement operations and asks whether suitable fullerene patch replacements exist.

References

Do there exist fullerene patch replacement operations that allow one to recover the underlying global symmetry?

— Extremal Asymmetric Depth of Planar Graphs and Hidden Near-Mirror Symmetries of IPR Fullerenes  (2609.02585 - Pastorek, 2 Sep 2026) in Section 7, “Concluding remarks”