Fulleroids are cubic convex polyhedra with faces of size 5 or greater. They are suitable models of carbon molecules. In this paper sufficient and necessary conditions for existence of fulleroids of tetrahedral symmetry types and with pentagonal and n-gonal faces only depending on number n are presented. Either infinite series of examples are found to prove existence or nonexistence is proved using symmetry invariants.
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Kardoš, F. Tetrahedral Fulleroids. J Math Chem 41, 101–111 (2007). https://doi.org/10.1007/s10910-006-9057-1
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DOI: https://doi.org/10.1007/s10910-006-9057-1