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arXiv · 1112.3320

Fullerene-like spheres with faces of negative curvature

Mathieu Dutour Sikiric·Michel Deza·Mikhail Shtogrin
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Abstract

Given R\subset N, an (R,k)$-sphere is a k-regular map on the sphere whose faces have gonalities i\in R. The most interesting/useful are (geometric) fullerenes, i.e., (\{5,6\},3)$-spheres. Call κ_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\le 3 (they are listed), icosahedrites (i.e., ({3,4},5)$-spheres) and, for any c\in N, fullerene c-disks, i.e., ({5,6,c},3)-spheres with p_c=1.

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Mathieu Dutour Sikiric, Michel Deza, Mikhail Shtogrin. 2011-12-14. Fullerene-like spheres with faces of negative curvature. https://arxiv.org/abs/1112.3320

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