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Fullerene-Like Spheres with Faces of Negative Curvature

  • Michel Deza
  • Mathieu Dutour Sikirić
  • Mikhail Shtogrin
Chapter
Part of the Carbon Materials: Chemistry and Physics book series (CMCP, volume 6)

Abstract

Given \(R \subset\mathbb{N}\), an (R, k)-sphere is a k-regular map on the sphere whose faces have gonalities iR. 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.

Keywords

Plane Graph Negative Curvature Plane Partition Regular Plane Plane Tiling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Michel Deza
    • 1
  • Mathieu Dutour Sikirić
    • 2
  • Mikhail Shtogrin
    • 3
  1. 1.Ecole Normale SuperieureParisFrance
  2. 2.Department of Marine and Environmental ResearchInstitut Rudjer BoskovicZagrebCroatia
  3. 3.Steklov Mathematical InstituteDemidov Yaroslavl State UniversityYaroslavl, MoscowRussia

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