Abstract Combinatorial techniques based on Sheehan’s modification of Pόlya’s theorem and Mȍbius inversion technique together with character cycle indices are applied to face colorings of giant fullerenes. These techniques are applied to icosahedral fullerenes, C80 with a chamfered dodecahedron structure, a chiral fullerene C140, icosahedral C180 and C240 with a chamfered truncated icosahedron geometry. The techniques are shown to provide both achiral and chiral face colorings of giant fullerenes for (a) coloring only pentagons with all hexagons painted white, (b) coloring hexagonal faces with all pentagons kept white, (c) both pentagons and hexagons painted with variable colors from a single set, and (d) both pentagons and hexagons painted with variable colors but chosen from two different sets. We have shown that in order to produce chiral colorings for the Ih fullerenes at least 2 black colors and remaining being white are needed when both pentagons and hexagons are varied. Results provide new insights into facial labeling and facial dynamics of fullerenes, while therefore being fully prepared to be inscribed in the new so called neutrosophical science (of carbon) nano-structural physical-chemistry.

中文翻译：

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二十面体巨富勒烯的面着色和手性面着色：C80 至 C240

摘要 基于 Sheehan 对 Pόlya 定理的修改和 Mȍbius 反演技术以及字符循环指数的组合技术应用于巨富勒烯的面着色。这些技术应用于二十面体富勒烯、具有倒角十二面体结构的 C80、手性富勒烯 C140、二十面体 C180 和具有倒角截头二十面体几何形状的 C240。这些技术被证明可以提供巨富勒烯的非手性和手性面着色，用于 (a) 仅将所有六边形涂成白色的五边形着色，(b) 将所有五边形都涂成白色的六边形面着色，(c) 五边形和六边形都涂有可变一组颜色，以及 (d) 五边形和六边形都涂有不同颜色但从两组不同的颜色中选择。我们已经表明，为了产生 Ih 富勒烯的手性着色，当五边形和六边形变化时，至少需要 2 种黑色并保持白色。结果为富勒烯的面部标记和面部动力学提供了新的见解，同时为被新的所谓中性科学（碳）纳米结构物理化学所铭记做好了充分的准备。