Abstract
Given \(R \subset\mathbb{N}\), an (R, k)-sphere is a k-regular map on the sphere whose faces have gonalities i ∈ R. The most interesting/useful are (geometric) fullerenes, that is, ({5, 6}, 3)-spheres. Call \({\kappa }_{i} = 1 + \frac{i} {k} - \frac{i} {2}\) the curvature of i-gonal faces. (R, k)-spheres admitting κ i < 0 are much harder to study. We consider the symmetries and construction for three new instances of such spheres: ({a, b}, k)-spheres with p b ≤ 3 (they are listed), icosahedrites (i.e., (3, 4, 5)-spheres), and, for any \(c \in\mathbb{N}\), fullerene c-disks, that is, ({5, 6, c}, 3)-spheres with p c = 1.
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Deza, M., Sikirić, M.D., Shtogrin, M. (2013). Fullerene-Like Spheres with Faces of Negative Curvature. In: Diudea, M., Nagy, C. (eds) Diamond and Related Nanostructures. Carbon Materials: Chemistry and Physics, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6371-5_13
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DOI: https://doi.org/10.1007/978-94-007-6371-5_13
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