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<p>The paper is an attempt to apply the theory of dessins d’enfants to the theory of fullerenes. The classical results concerning the calculation of the dodecahedron Belyi function are presented and then applied to the calculation of the Belyi function of the barrel, and the Euclidean geometry of the latter is investigated. The non-existence of a&#xa0;fullerene with the only hexagonal face is established by the methods of dessins d’enfants.</p>

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FULLERENES AND BELYI FUNCTIONS

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • N. M. Adrianov,
  • G. B. Shabat

摘要

The paper is an attempt to apply the theory of dessins d’enfants to the theory of fullerenes. The classical results concerning the calculation of the dodecahedron Belyi function are presented and then applied to the calculation of the Belyi function of the barrel, and the Euclidean geometry of the latter is investigated. The non-existence of a fullerene with the only hexagonal face is established by the methods of dessins d’enfants.