Fullerene-like spheres with faces of negative curvature

2011/12/14 by Mathieu Dutour Sikirić, Sikiric, Mathieu Dutour, Michel Deza +3 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1112.3320

openalex publication_date 2011/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given R⊂ 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, i.e., (\5,6\,3)-spheres. Call κ_i=1 + (i)/(k) - (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∈ N, fullerene c-disks, i.e., (5,6,c,3)-spheres with p_c=1.

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