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arXiv · 2607.21483

Symmetries of (3, 6)-Fullerenes

Linda E Green·Yadunand Sreelesh·Vibhu Gomatam
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Abstract

A (3, 6)-fullerene is a cubic planar graph whose faces all have 3 or 6 sides. We give an exact enumeration of (3, 6)-fullerenes with V vertices and each of five possible symmetry types: *332, 332, 2*2, *222, and 222, in orbifold notation. We use this enumeration, together with some constructions, to resolve three conjectures about the existence of (3, 6)-fullerenes with 2*2$, *222, and 222 symmetry for given numbers of vertices.

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Linda E Green, Yadunand Sreelesh, Vibhu Gomatam. 2026-07-23. Symmetries of (3, 6)-Fullerenes. https://arxiv.org/abs/2607.21483

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