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Manifolds of Spherical Tessellations

  • José María Montesinos-Amilibia
Chapter
Part of the Universitext book series (UTX)

Abstract

The spherical tessellations are represented by the platonic solids or regular polyhedra. Thus the set of positions of a platonic solid inscribed in the 2-sphere S2 is a closed 3-manifold. The fundamental group of such a manifold is an extension of ℤ2 by the group of isometries of the platonic solid. The subgroup ℤ2 is the center of the group. The manifold can be thought of as the spherical tangent bundle of a 2-dimensional spherical orbifold, or as a 3-dimensional spherical orbifold, i.e. the quotient of S3 under a finite subgroup of SO(4). Some material of this chapter was borrowed in part from [DuV].

Keywords

Fundamental Domain Stereographic Projection Lens Space Solid Torus Finite Subgroup 
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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References

  1. Dumbar, W.: [Dui]Google Scholar
  2. Du Val, P.: [DuV]Google Scholar
  3. Lamotke, K.: Regular solids and isolated singularities. Vieweg Advanced Lectures in Math. Braunschweig-Wiesbaden: Friedr. Vieweg u, Sohn 1986Google Scholar
  4. Scott, P.: [Sc]Google Scholar
  5. Slodowy, P.: [S1]Google Scholar
  6. Threlfall, W., Seifert, H.: [TS]Google Scholar
  7. WOLF, J.A.: Spaces of constant curvature. Berkeley, Cal.: Publish or Perish 1977Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • José María Montesinos-Amilibia
    • 1
  1. 1.Facultad de MatemáticasUniversidad ComplutenseMadridSpain

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