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Tessellations of Compact Surfaces

  • John Stillwell
Part of the Universitext book series (UTX)

Abstract

Poincaré’s theorem for a compact polygon II satisfying the side and angle conditions tells us that the identification space SII, obtained by identifying sides of II according to the side pairing, is also an orbit space S/Γ. Here S = SII is S2, ℝ2, or ℍ2—the surface from which II originates—and Γ is the group generated by the side-pairing transformations of II. Because of its interpretation as an orbit space, SII is also called an orbifold.

Keywords

Orbit Space Finite Index Cone Point Compact Surface Geometric Surface 
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 New York 1992

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Mathematics DepartmentMonash UniversityClaytonAustralia

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